Answer
a. $x=2; x=-1$
b. $x=4; x=-3$
Work Step by Step
The original function is $f(x)=2x^3-3x^2-12x+4$ therefore, $f'(x)=6x^2-6x-12$
a. Set the derivative function equal to 0 because the slope of a horizontal line is 0:
$6x^2-6x-12=0$
$6(x^2-x-2)=0$
$6(x-2)(x+1)=0$
$x=2; x=-1$
b. Set the derivative function equal to 60:
$6x^2-6x-12=60$
$6x^2-6x-72=0$
$6(x^2-x-12)=0$
$6(x-4)(x+3)=0$
$x=4; x=-3$