Question

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

Answer 1

Decreasing.

Explanation:

The sign (positive/negative) of the first derivative of a function tells if the function is increasing or decreasing at a point.

• If `f'(-2)<0`, then `f(x)` is decreasing at `x=-2`.

• If `f'(-2)>0`, then `f(x)` is increasing at `x=-2`.

To find the derivative of the function, use the power rule.

`f(x)=x^2-3x`

`f'(x)=2x-3`

Find the sign of the derivative at `x=-2`.

`f'(-2)=2(-2)-3=-7`

Since `f'(-2)<0`, the function is decreasing at `x=-2`.

We can check by consulting a graph:

graph{x^2-3x [-5, 7, -4.02, 21.65]}