Question

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

Answer 1

decreasing at x = - 1

Explanation:

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

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

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

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

`rArrf'(x)=-3x^2+6x-1`

`rArrf'(-1)=-3(-1)^2+6(-1)-1=-10`

Since f'(-1) < 0 , then f(x) is decreasing at x = -1
graph{-x^3+3x^2+6x-1 [-50.76, 50.76, -25.4, 25.36]}