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

1 Answer
Jun 27, 2018

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