Critical Points?

[legacyofpiracy]

Our teacher just covered 3 sections in two days so there are still a few parts that I am struggling with. I came across one of these while I was trying to do the homework, it was asking me to find the sum of all the x values of the critical points of this equation:

f'(x)=(x^2-11x+24)/(x+1)


It seems like this should be relatively simple but i am just having trouble getting started, any suggestions?

 

[stapel]

Are you supposed to find the critical values of f'(x), so you're finding the second derivative, or are you supposed to find the critical values of f(x), so you can start right to work with f'(x)?

Thank you.

Eliz.

 

[legacyofpiracy]

The problem asked for the critical values of f'(x). So yes I think i am finding the second derivative.

 

[stapel]

Okay, so apply the Quotient Rule to find the second derivative. Then recall that a fraction is zero when the numerator is zero, and set the numerator equal to zero. Solve for the critical points of f'(x).

Eliz.

 

[legacyofpiracy]

How are you supposed to get two critical values then? Sorry this might be a silly question.

 

[stapel]

How are you supposed to get two critical values then?

What is the derivative of f'(x)? Let's work from that.

Eliz.

 

[tkhunny]

You MAY wish to simplify your life are restate the expression:

\(\displaystyle f(x)\,=\,x\,-\,12\,+\,\frac{36}{x+1}\)