Calculus 1 Critical Point and Local Extrema

Question

I'm not even sure where to start, here is the question.

If a is a positive constant, find all critical points of f(x)=x^3−ax.

b) find the value of a so that f has a local extrema at x=+-2

Answer 1

The critical points are where the derivative of f = 0:

f'(x) = 3x² - a = 0

Solving for x: x² = a/3

x = +/- sqrt(a/3)

Since x has local extreme at +/- 2, set x = -2 and +2:

2 = sqrt(a/3)

Solving for a:

4 = a/3

a = 12