# What are the critical points of f(x) =e^(e^x)?

Nov 10, 2015

No critical points.

#### Explanation:

Critical points occur when the derivative of the function is zero or undefined.

In this case, $\frac{d}{\mathrm{dx}} \left({e}^{{e}^{x}}\right) = {e}^{x} \cdot {e}^{{e}^{x}} = {e}^{x + {e}^{x}} \ne 0 \forall x \in \mathbb{R}$

Hence there are no critical points. The graph of the function also verifies this.

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