# How do you find local maximum value of f using the first and second derivative tests: f(x) = 7e^x?

$I f a < b \mathmr{and} x \in \left[a , b\right] , \min f \left(x\right) = 7 {e}^{a} \mathmr{and} \max f \left(x\right) = 7 {e}^{b}$
The function remains the same upon differentiation, any number of times. This is a characteristic of ${e}^{x}$.
For all x, ${e}^{x} > 0$. So are the derivatives.
$\frac{d}{\mathrm{dx}} f \left(x\right) > 0$. So, $7 {e}^{x}$ is an increasing function, from 0 to infinity. through 7 at x = 0..