The diagram displays the curve $y = e^x + 4e^{-2x}$ together with its minimum point $M$.
(i)[3]
Show that the $x$-coordinate of $M$ equals $\ln 2$.
(ii)[4]
The shaded region shown in the diagram is enclosed by the curve and the lines $x = 0$, $x = \ln 2$ and $y = 0$. Use integration to show that the area of the shaded region is $\frac{5}{2}$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to give $e^x - 8e^{-2x}$” …