Find the absolute maximum and absolute minimum values of $f$ on the given interval.
$f(x) = 4x^3 - 6x^2 - 144x + 8$, $[-4, 5]$
Step 1
The absolute maximum and minimum values of $f$ occur either at a critical point inside the interval or at an endpoint of the interval. Recall
We begin by finding the derivative of $f$.
$f'(x) = 12x^2 - 12x - 144$
Step 2
We now solve $f'(x) = 0$ for $x$, which gives the following critical numbers. (Enter your answers as a comma-separated list.)
$x = -3, 4$
Step 3
We must now find the function values at the critical numbers we just found and at the endpoints of the interval $[-4, 5]$.
$f(-3) = 278$
$f(4) =$
$f(-4) =$
$f(5) =$
