The curve is given by $y=k\sqrt{4x+1}-x+5$, where $k$ is a positive constant.
(a)[2]
Find $\frac{dy}{dx}$.
(b)[2]
Find the $x$-coordinate of the stationary point in terms of $k$.
(c)[4]
Given that $k = 10.5$, find the equation of the normal to the curve at the point where the tangent to the curve makes an angle of $\tan^{-1}(2)$ with the positive $x$-axis.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate differentiation by the chain rule” …