f(x)=(9-x^2)^3/5

[Jade]

Considering the function in the subject line I conclude that

f'(x)=3/5(9-x^2)^-2/5(-2x)

What is the best way to simplify this? For what x, the tangent line to f(x) is horizontal and not differentiable?

 

[galactus]

\(\displaystyle \L\\\frac{-6x}{5(9-x^{2})^{\frac{2}{5}}}=0\)

What values of x make this equal to 0?. It's easy to see, isn't it?.

 

[Jade]

Critical Numbers

-6x=0

9-x^2=0

x=0,3

For what x, the tangent line to f(x) is horizontal? I think I am having a problem with when I get the critical numbers what do I do with them to help me answer the rest of the questions.

 

[pka]

There is no division by zero!
Therefore, one of those answers is wrong.

 

[Jade]

Sub zero into original function

f(x)=(9-0^2)^3/5