# Thread: absolute maximum and minimum

1. ## absolute maximum and minimum

I have one more of these problems that I got stuck on:

Help Plz?

2. What have you done so far?

You take the derivative and set it to zero. Solve for x, this will give you all critical points. From here you can look at the second derivative at those points to determine if they are maximums or minimums. If $\displaystyle \frac{d^2f(x)}{dx^2} < 0$ then the point is a maximum. If $\displaystyle \frac{d^2f(x)}{dx^2} > 0$ then the point is a minimum. If $\displaystyle \frac{d^2f(x)}{dx^2} = 0$ then the point is a neither. Don't forget to determine the value $\displaystyle f(x)$.

3. thats the problem, I know I don't have the right derivative. We are just learning them, and Im not sure how to do it. After I get the derivative I'm fine, but I need help with getting that.

I know that after I set my values equal to zero, I just take those values and plug them in the derivative.

4. Okay, you will use the quotient rule, i.e.,
$\displaystyle f'(x) = \frac{\frac{d}{dx}\left[-x^3 + x^2 + 3x + 1\right]\cdot (x+1) + \frac{d}{dx}\left[x+1\right]\cdot (-x^3 + x^2 + 3x + 1)}{(x+1)^2}$.
Can you take it from here?