Question

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

Answer 1

I found that it is increasing.

Explanation:

We can try evaluating the derivative of the function at `x=3` that gives us the inclination of the function:
`f'(x)=(2x-1)e^(x^2-x)-2x`
At `x=3`:
`f'(3)=(6-1)e^(9-3)-6=5e^6-6=2011>0` so increasing.