The graph depicts the curve given by $y = \frac{2\ln x}{3x + 1}$. It meets the $x$-axis at $A$ and reaches a maximum at $B$. The shaded area is enclosed by the curve together with the lines $x = 3$ and $y = 0$.
(a)[3]
Determine the gradient of the curve at $A$.
(b)[3]
Use calculation to show that the $x$-coordinate of $B$ is between $3.0$ and $3.1$.
(c)[3]
Apply the trapezium rule over two intervals to estimate the area of the shaded region. State 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: “Apply the quotient rule (or the product rule) to differentiate” …