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Math Help - A couple of quick calculus questions...

  1. #1
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    Question A couple of quick calculus questions...

    I think I have these figured out, but just want to check...
    1. Let f and g be functions that are differentiable for all real numbers. Let g(x)=f(x^2). Find g'(x). I came up with 2x * f'(x^2). Is this correct?

    2. Let g(x)=3x^5-5x^4. Find the number of extreme points on teh graph of g(x). I found 2 extreme points when I entered this function into my calculator. Right or not?

    Thanks for the help in advance!
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  2. #2
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    Quote Originally Posted by bemidjibasser View Post
    I think I have these figured out, but just want to check...
    1. Let f and g be functions that are differentiable for all real numbers. Let g(x)=f(x^2). Find g'(x). I came up with 2x * f'(x^2). Is this correct?

    2. Let g(x)=3x^5-5x^4. Find the number of extreme points on teh graph of g(x). I found 2 extreme points when I entered this function into my calculator. Right or not?

    Thanks for the help in advance!
    The first one is correction.

    For the second one differentiate it.

     g'(x) = 15x^4-20x^3

    To find extreme points, set the derivative equal to zero and solve:

     g'(x) = 15x^4-20x^3 = 0

     x^3(15x-20) = 0

    So either  x = 0 \text{ or } x = \frac{4}{3} . 2 extreme points.
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