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

1. ## 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!

2. Originally Posted by bemidjibasser
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.