The diagram displays the curve with equation $y = \frac{2\ln x}{3x + 1}$. It cuts the $x$-axis at point $A$ and reaches a maximum at point $B$. The shaded area is enclosed by the curve and the lines $x = 3$ and $y = 0$.
(a)[3]
Find the gradient of the curve at $A$.
(b)[3]
Show by calculation that the $x$-coordinate of $B$ lies between $3.0$ and $3.1$.
(c)[3]
Use the trapezium rule with two intervals to estimate the area of the shaded region. Give your answer correct to 2 decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate using quotient rule (or product rule)” …