# What are the extrema of f(x) = 7e^x?

Oct 27, 2016

There are no extrema

#### Explanation:

$f \left(x\right) = 7 {e}^{x}$
$\therefore f ' \left(x\right) = 7 {e}^{x}$

At a max/min, $f ' \left(x\right) = 0 \implies 7 {e}^{x} = 0$
$\therefore {e}^{x} = 0$

But ${e}^{x} > 0 \forall x \in \mathbb{R}$

Hence there are no extrema!