Exponential is Strictly Increasing

Theorem
Let $x \in \R$ be a real number.

Let $\exp x$ be the exponential of $x$.

Then:
 * The function $f \left({x}\right) = \exp x$ is strictly increasing and convex.

Proof
We have that the exponential function is the inverse of the natural logarithm function:

We also have:
 * Inverse of Convex Strictly Monotone Function
 * $\ln x$ is strictly increasing and concave.

Hence the result.