(i)[3]
Show that $\dfrac{dy}{dx}$ is negative for every value of $x$.
(ii)[4]
The gradient of the curve is $-1$ when $x = a$. Prove that $a$ satisfies $e^{2a} - 4e^{a} + 1 = 0$. Hence determine the exact value of $a$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is defined by $y = \dfrac{1 + e^{-x}}{1 - e^{-x}}$, with $x > 0$.