Question

Is `f(x)=-2x^3+4x^2-3x-1` increasing or decreasing at `x=0`?

Answer 1

f(x) is decreasing at x = 0

Explanation:

To determine if f(x) is increasing/decreasing at x = 0 consider.

• If f'(0) > 0 , then f(x) is increasing

• If f'(0) < 0 , then f(x) is decreasing

differentiate f(x) using the `color(blue)"power rule"`

`rArrf'(x)=-6x^2+8x-3`

and `f'(0)=0+0-3=-3<0`

Since f'(0) < 0 , then f(x) is decreasing at x = 0
graph{-2x^3+4x^2-3x-1 [-10, 10, -5, 5]}