Question

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

Answer 1

`f` is increasing at `x=2`

Explanation:

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

Let `u=x^2-x` , `(du)/dx=2x-1`

`f(x)=ue^u`

`f'(x)=color(blue)(d/dx)ue^u=(du)/dxe^u+ue^u(du)/dx=(du)/dxe^u(u+1)`

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

`f'(2)=(4-1)(e^2)(3)=9e^2`

`f` is increasing at `x=2`