Question

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

Answer 1

Increasing.

Explanation:

If `f'(a)<0`, then `f(x)` is decreasing at that point.
If `f'(a)>0`, then `f(x)` is increasing at that point.

Find `f'(x)`—recall that `d/dx[x^n]=nx^(n-1)`.

`f'(x)=-4x-3`

`f'(-2)=-4(-2)-3=5`

Since `5>0,f(x)` is increasing when `x=-2`.