Applications of Differentiation

MA-C3 is worth about 16 marks out of 100 in recent HSC Mathematics Advanced papers. Practise 48 exam-style questions (multiple choice, multi-part, algebraic answer, numerical answer) with instant marking and a worked solution for every question.

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Example questions

Example 1 · 1 mark · multiple choice

At which $x$ -values does $y = x^{3} - 12 x + 1$ have stationary points?

A $x = - 2$ and $x = 2$
B $x = - 23$ and $x = 23$
C $x = 0$ only
D $x = 2$ only

Example 2 · 1 mark · multiple choice

Given $f^{'} (x) = (x + 1) (x - 3)$ , on which interval is $f (x)$ decreasing?

A $x < - 1$
B $- 1 < x < 3$
C $x > 3$
D $x < - 1$ or $x > 3$

Example 3 · 1 mark · multiple choice

Water drains from a tank so that the volume $V$ litres after $t$ minutes is

V = 200 - 4 t + 0.02 t^{2}, 0 \leq t \leq 100.

How is the volume changing when $t = 25$ ?

ADecreasing at 3 litres per minute
BIncreasing at 3 litres per minute
CDecreasing at 4 litres per minute
D112.5 litres

Answers and worked solutions appear when you practise these questions.

Applications of Differentiation

Example questions

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