Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The function has rule $f(x) = \frac{4}{x^3} - \frac{3}{x} + 2$ for $x \neq 0$. Its graph, $y = f(x)$, is displayed in the diagram.
(a)[5]

Find the set of values of $x$ for which $f(x)$ is decreasing.

(b)[8]

A triangle is formed by the $y$-axis, the normal to the curve at the point where $x = 1$ and the tangent to the curve at the point where $x = -1$. Find the area of the triangle. Give your answer correct to 3 significant figures.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Derivative correctly given as $\frac{dy}{dx}=\frac{12}{x^4}+\frac{3}{x^2}$

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