Question

Is `f(x)=(1-e^x)/(1-x^2)` increasing or decreasing at `x=2`?

Answer 1

the first derivative is negative. The function is decreasing.

Explanation:

The first derivative of f is `((1-x^2)(-e^x) -(1-e^x)(-2x))/(1-x^2)^2`
its sign is the same as the sign of its numerator which is
`3e^2 + 4 (1-e^2) = -e^2 + 4 <0`

It is negative thus the function is decreasing at `x=2`

graph{(1-e^x)/(1-x^2) [-10, 10, -5, 5]}