Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve defined by $6e^{2x} + ke^x + e^{2y} = c$, where $k$ and $c$ are constants, passes through the point $P$ with coordinates $(\ln 3, \ln 2)$.

(i)[2]

Show that $58 + 2k = c$.

(ii)[5]

Given also that the gradient of the curve at $P$ is $-6$, find the values of $k$ and $c$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use any one of $e^{2x}=9$, $e^y=2$, $e^{2y}=4$” …