Question

Consider the function below f(x) = x3 − 12x + 3 find intervals of increase and decrease

Answer 1

Turning points are where the derivative is zero.
f'(x) = 0 = 3x² -12
0 = 3(x -2)(x +2)
The values of x that satisfy this are x=2, x=-2.

Since the coefficient of x³ is positive, we know the function is generally increasing left-to-right. It will have an interval of decrease between the turning points.

increasing: (-∞, -2) ∪ (2, ∞)
decreasing: (-2, 2)