Find the max value of a function at a given interval

Question

Trying to determine local max for a function at interval $[-4, 6]$. $$f(x)= x^3 -3x^2-24x + 7$$

Is the proper next step to take the derivative of $f(x)$ and find the roots, set roots = to zero?

Answer 1

Hints:

• Take the derivative, find the zeros, test those points. You should get $x = -2, 4$ (a Min and a Max).
• Plot the function and verify.

Answer 2

Yes, find $f'(x) =0, x \in [-4,6]$, then test the zeros and the endpoints of your interval.

Answer 3

$f'(x)=3x^2-6x-24$. Now, you get the maximum point when $f'(x)=0$. That is when $x=-2$ or $x=4$.

Now, in order to know if it is a minimum or maximum, notice that your function is positive from [$-2,0$] and negative from [$0,6$]. Therefore, $x=-2$ is the maximum you are looking for ($x=4$ is a minimum.)