Level 3 Differentiation Walkthrough

2025 NCEA Level 3 Differentiation Question 3(a)

2025 Paper

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Question

The graph below shows the function \(y=f(x)\).

x y
\[ \text{(i) Find the value(s) of }x\text{ where }f(x)\text{ is not differentiable.} \] \[ \text{(ii) Find the value(s) of }x\text{ where }f'(x)=0. \] \[ \text{(iii) What is the value of }\lim_{x\to -2}f(x)\text{?} \]

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First walkthrough idea

Hint to try first

Points are not differentiable where the graph has a jump, a hole, or a sharp break.

Step 1

Find the non-differentiable points

There is a break at \(x=-6\), a hole and mismatched point at \(x=-2\), and another hole at \(x=3\).

Show the first step’s working

There is a break at \(x=-6\), a hole and mismatched point at \(x=-2\), and another hole at \(x=3\).

Key result

\[ x=-6,\,-2,\text{ and }3 \]

Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Reading differentiability, stationary points, and a limit from a graph.

This is Question 3(a) from the 2025 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 reading differentiability, stationary points, and a limit from a graph. 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

← Question 2(e) Question 3(b) →