Level 3 Differentiation Walkthrough

2022 NCEA Level 3 Differentiation Question 1(b)

2022 Paper - Stationary points

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Question

Find the \(x\)-value(s) of any stationary points on the graph of \(f(x)=\frac{x^2+1}{x}\).

You must use calculus and show any derivatives that you need.

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

First walkthrough idea

Tip to try first

Stationary points happen where the gradient is zero, so you will need \(f'(x)\).

Step 1

Identify the differentiation rule

Reveal the explanation and working for this step.

Show the first step’s working

This function is written as one expression divided by another.

Key result

Quotient rule

This is a quotient, so the quotient rule is the best method here.

Walkthrough overview

What this question practises

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

Method: Finding and interpreting stationary points.

This is Question 1(b) 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 finding and interpreting stationary points. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

After solving the derivative condition, check the point's nature and answer the conclusion the question actually asks for.

Continue practising

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