Question

Is `f(x)=(x-2)(2x-3)(2x-1)` increasing or decreasing at `x=-2`?

Answer 1

Increasing.

Explanation:

Calculate the first derivative when `x=-2`. If the value is negative, the function is decreasing at that point.If the value is positive, the value is increasing at that point.

First, to avoid doing annoying three-pronged product rule, distribute the binomials.

`f(x)=4x^3-16x^2+19x-6`

`f'(x)=12x^2-32x+19`

`f'(-2)=48+64+19`

`f'(-2)` is positive, so the function is increasing at this point.