Using a calculator or computer, sketch the graph of $y = 2 e^x + 4 e^{-x}$ for $-3 \le x \le 3$, $0\le y\le 20$. Observe that it looks like the graph of $y=\cosh x$.

Approximately where is its minimum?
Minimum at $x =$

Show algebraically that $y = 2 e^x + 4 e^{-x}$ can be written in the form $y=A\cosh (x-c)$. Calculate the values of $A$ and $c$.
$A =$
$c =$
(Think what this tells you about the graph you obtained!)