Question

Find the interval [a, b] on which the function f(x) = 2 x3+3 x2−12 x+3 is decreasing. Enter your answer as: [a, b] for some constants a, b.

Answer 1

f(x) is decreasing when f'(x) < 0, so just solve

6x^2+6x-12 < 0
x^2+x-2 < 0
(x+2)(x-1) < 0

The roots are at -2 and 1, and the parabola opens upward, so f'(x) < 0 between the roots.

f(x) is decreasing on (-2,1)

Note that it is not [-2,1] because at the endpoints, f(x) is a max or min, and so is not changing.