Question

Is `f(x)=cosx/(pi-e^x)` increasing or decreasing at `x=pi/6`?

Answer 1

Increasing.

Explanation:

`d/dxf=((sqrt3+1)e^(pi/6)-pi)/(2(pi-e^(pi/6))^2)`.
Numerator at x = `pi/6` is 1.470.....>0
The first derivative is > 0..