# What are the critical points of # f(x) = x*sqrt(8-x^2) #?

##### 1 Answer

x=

#### Explanation:

To find the critical points of a function, find where the first derivative equals 0.

For

You need to use the product rule for derivatives:

where in this case,

It is easier to represent

Now use the Chain Rule to find the derivative of

(**Don't forget to find the derivative of the inside function --**

*that's*where the

Clean this up so

OKAY, put it all together now:

Combine these two fractions into one by getting common denominators and you get

Critical values occur when

numerator = 0 and/or denominator = 0).

Setting the numerator = 0 and solving results in

Setting the denominator = 0 and solving results in

If you use Symbolab, you can quickly get these answers, I hope my explanation helped! :)