Level 3 Differentiation Walkthrough

2022 NCEA Level 3 Differentiation Question 2(c)

2022 Paper - Stationary time from a displacement function

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Question

\[ d(t)=\frac{t^2-6}{2t^3}, \qquad t>0 \]

Find the time(s) when the object is stationary.

You must use calculus and show any derivatives that you need when solving this problem.

A later walkthrough visual becomes available with JavaScript; the complete question and first learning steps remain below.

First walkthrough idea

Tip to try first

Because the displacement is written as a fraction, start with the quotient rule.

Step 1

Identify the differentiation rule

Reveal the explanation and working for this step.

Show the first step’s working

Use the quotient rule because the displacement function is a fraction.

Key result

Quotient rule

The function is written as one expression divided by another, so the quotient rule is a good starting point.

Walkthrough overview

What this question practises

This 2022 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Quotient rule and finding when motion is stationary.

This is Question 2(c) from the 2022 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise quotient rule and finding when motion is stationary. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Use brackets carefully and retain the squared denominator when applying the quotient rule.

Continue practising

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