Methods2024 Exam 1 · Q8Tech-free7 marks

Cube root function: intercept and equal gradients

Let $g: \R \to \R, g(x) = \sqrt[3]{x-k} + m$ , where and .

Find the coordinates of $P$ , in terms of $k$ and $m$ .

1 mark

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Find the gradient of $g$ at $P$ , in terms of $k$ .

2 marks

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Given that the graph of $y = g(x)$ passes through the origin, express $k$ in terms of $m$ .

1 mark

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Let the point $Q$ be a point different from the point $P$ , such that the gradient of $g$ at points $P$ and $Q$ are equal.

Given that the graph of $y = g(x)$ passes through the origin, find the coordinates of $Q$ in terms of $m$ .

3 marks

Hints, answer checking and worked solutions come with a Season Pass.