The diagram illustrates a section of the curve whose equation is $y = \frac{5x}{4x^3 + 1}$. The shaded area is enclosed by the curve together with the lines $x = 1$, $x = 3$ and $y = 0$.
(a)[4]
Find $\frac{dy}{dx}$ and hence determine the $x$-coordinate of the maximum point.
(b)[3]
Use the trapezium rule with two intervals to estimate the area of the shaded region. Give your answer correct to 2 significant figures.
(c)[1]
State, with a reason, whether your answer to part (b) is an over-estimate or under-estimate of the exact area of the shaded region.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate with quotient rule (or product rule)” …