Question

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

Answer 1

f(x) is increasing at x = 1

Explanation:

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

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

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

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

and `f'(1)=-2(1)+3=1`

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