Question

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

Answer 1

f(x) is increasing at x=2.

Explanation:

The test is that if f' (x) is positive at x=2 then it is increasing otherwise decreasing. If f'(x)=0 then it neither increasing or decreasing.

In this case f'(x) =

At x=2, f ' (x)=`(3/4) e^2` which is positive. Hence f(x) is increasing at x=2.