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| More maths help... | |
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| Tweet Topic Started: Jun 7 2006, 10:54 AM (299 Views) | |
| ***musical princess*** | Jun 7 2006, 10:54 AM Post #1 |
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HOLY CARP!!!
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Sorry... ![]() Okay, first off, am i right in theinking that if you are differentiating an inverse function, you can just swap the x's and y's and differentiate as normal? Secondly, i'm a bit confused with this (what's new ). If i give an example it might be easier...Given that y=(x^2 -4)^3 ... i) find dy/dx ii) find the co-ordinates of any stationary points and determine their nature. So, i can do the first part fine. Just by using the chain rule (dy/dx=dy/du x du/dx) and i get the answer to equal: dy/dx=6x(x^2 -4)^2 It's the next part i dont get. I know i have to put it equal to 0 to find the stationary points and then differentiate AGAIN to find the nature, but i'm not sure how i differentiate the 6x(x^2 -4)^2....? Am i supposed to use the chain rule again?? Sorry to keep pestering but you don't know how much this is helping me! My exam is tomorrow morning!!!! ![]() x |
| x Caroline x | |
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| JBryan | Jun 7 2006, 10:57 AM Post #2 |
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I am the grey one
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You could multiply out the (x^2-4)^2, multiply through by 6x and differentiate that. There is another way but I think it would be harder in the long run. |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| ***musical princess*** | Jun 7 2006, 11:00 AM Post #3 |
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HOLY CARP!!!
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I was thinking that at first but it seems extremely long winded... x |
| x Caroline x | |
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| Aqua Letifer | Jun 7 2006, 11:00 AM Post #4 |
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ZOOOOOM!
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Either that, or use the multiplication rule and chain rule together. Both should give the right answer. And with an inverse function, I'd just work it out as usual, although there is some trick to differentiating them. I myself never used it, though; never found the need. |
| I cite irreconcilable differences. | |
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| ***musical princess*** | Jun 7 2006, 11:01 AM Post #5 |
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HOLY CARP!!!
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So use chain rule on the brackets then multiply by 6x? x |
| x Caroline x | |
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| Aqua Letifer | Jun 7 2006, 11:01 AM Post #6 |
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ZOOOOOM!
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:lol: The last math exam I remember taking was 3 hours long, and consisted of 2 problems; we all barely got done in time. Math = long-winded. EDIT Well, use whatever you're more comfortable with. You do know what I mean by multiplication rule, right? Treat the 6x and the rest as two seperate entities multiplied together. Or, like JB said, expand the factors and make it one long polynomial chain. Both should give you the same answer. Heck, if you're studying for an exam, this would be a good way to check yourself; try it both ways and see what develops! |
| I cite irreconcilable differences. | |
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| JBryan | Jun 7 2006, 11:03 AM Post #7 |
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I am the grey one
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(x^2-4)^2 is simply x^4 - 8x^2 + 16. Multiply through by 6x: 6x^5 - 48x^3 + 96x. I did that in my head in just a minute or so. |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| ***musical princess*** | Jun 7 2006, 11:12 AM Post #8 |
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HOLY CARP!!!
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Okay... so then i've got that, where do i go from there? And, what would i do if it had been raised to a high power like 6 or 7 and i couldn't mulitply it out? x |
| x Caroline x | |
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| JBryan | Jun 7 2006, 11:22 AM Post #9 |
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I am the grey one
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Power Rule + Product Rule |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| JBryan | Jun 7 2006, 11:25 AM Post #10 |
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I am the grey one
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differentiate again and substitute the stationary points. Whether the result is positive or negative will give you the nature (concave/convex) |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| ***musical princess*** | Jun 7 2006, 11:31 AM Post #11 |
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HOLY CARP!!!
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I know what to do, i just don't know how to do it. Like, how do i get to the co-ordinates from the differential. I know you put it equal to 0 but i don't have a clue how i would get what x equals. I am so screwed. ![]() x |
| x Caroline x | |
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| JBryan | Jun 7 2006, 11:34 AM Post #12 |
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I am the grey one
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In the first derivative you find the values of x that make the function equal zero. For 6x(x^2-4)^2 those values are 0 and 2. |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| Aqua Letifer | Jun 7 2006, 11:35 AM Post #13 |
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ZOOOOOM!
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Yep, and so then you put those two x values, 0 and 2, into the original equation, and then find the y values for each. That will give you the coordinates. |
| I cite irreconcilable differences. | |
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| ***musical princess*** | Jun 7 2006, 11:40 AM Post #14 |
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HOLY CARP!!!
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This might sound like an uber dumb question, but how did you get those values? x |
| x Caroline x | |
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| JBryan | Jun 7 2006, 11:42 AM Post #15 |
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I am the grey one
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6x = 0 :. x = 0. x^2-4 = 0 x^2 = 4 x = 2 |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| Aqua Letifer | Jun 7 2006, 11:43 AM Post #16 |
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ZOOOOOM!
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EDIT Okay, JB's on top of it. All good. |
| I cite irreconcilable differences. | |
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| ***musical princess*** | Jun 7 2006, 11:44 AM Post #17 |
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HOLY CARP!!!
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Oooooh!!! ![]() :rolleyes: So obvious when someone points it out! ![]() ![]() Do you want to sit my exam for me, JBryan? Please? x |
| x Caroline x | |
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| JBryan | Jun 7 2006, 11:49 AM Post #18 |
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I am the grey one
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Rather a long commute for me and I suspect I could not be taken for you. In fact, it would be impossible. Besides, what if I flunk?
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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| ***musical princess*** | Jun 7 2006, 11:52 AM Post #19 |
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HOLY CARP!!!
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You wouldn't! We could dress you up as me and you could wear a wig!! No-one would know any difference!!! Seriously, thankyou so much. ![]() (and you too, Aqua )x |
| x Caroline x | |
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| FrankM | Jun 7 2006, 01:47 PM Post #20 |
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Senior Carp
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mp, I don't want to overload you with information at the eleventh hour here. But I assume you know the basic differentiation formulas. What often trips people up is not the differentiation itself but the solving for x in equations of the form (1) F(x) = 0 First I assume you're capable of rearranging any equation in a single variable to get all the non-zero terms on one side and zero on the other side as in eq (1). Next, note that if the rearranged equation comes out as a chain product of functions, that is, you get, for example, F(x) = g(x)h(x)p(x) = 0 Then the solutions to g(x) = 0 h(x) = 0 and p(x) = 0 are all valid solutions to eq (1). But how do you get solutions to any of these equations? Well, if the equation contains no higher power of x than unity, you can always arrange it into the form of some constant times x, that is, Kx = 0 Then clearly x = 0 is a solution. What if the highest power of x is 2? Then we can use the general quadratic solution. I assume you're familiar with that. That is, given the general quadratic form ax^2 + bx + c = 0, we have the standard pair of solutions: x = [– b + SQRT(b^2 – 4ac)]/2a and x = [– b – SQRT(b^2 – 4ac)]/2a Example: 3x^3 – 16x^2 + 12x = 0 But the highest power is a cube, so it seems we can't apply the standard quadratic solution. However, we note that the lowest power of x is unity, that is, there is no constant term. So we factor the cubic equation to obtain 3x(x^2 – 5x + 4) = 0 From the factor 3x we obtain one solution to be 3x = 0 and so x = 0. From the factor x^2 – 5x + 4 we obtain two quadratic equation solutions: x = [5 + SQRT(25 – 16)]/2 = [5 + SQRT(9)]/2 = [5 + 3]/2 = 8/2 = 4 x = [5 – SQRT(25 – 16)]/2 = [5 – SQRT(9)]/2 = [5 – 3]/2 = 1 |
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| ***musical princess*** | Jun 7 2006, 01:53 PM Post #21 |
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HOLY CARP!!!
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Oooo! I never even thought of using the forumla!! Of course! If i put it into a factorised form it is much easier! Thankyou Frank!! ![]() Bedtime now! Big day tomorrow! ![]() x |
| x Caroline x | |
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| Ballyhoo | Jun 7 2006, 03:19 PM Post #22 |
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Middle Aged Carp
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Don't forget x = -2 as well! |
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| JBryan | Jun 7 2006, 06:12 PM Post #23 |
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I am the grey one
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Right you are. |
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"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it". Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody. Eleanor: At my age there's not much traffic anymore. From The Lion in Winter. | |
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). If i give an example it might be easier...









5:00 PM Jul 10