Level 3 Differentiation Walkthrough
2023 NCEA Level 3 Differentiation Question 3(b)
2023 Paper
Question
The graph below shows the function \(y=f(x)\).
First walkthrough idea
Hint to try first
Continuous but not differentiable means the graph is joined up but has a sharp corner.
Step 1
Find the continuous corner
The graph meets at \(x=8\), but it does so with a sharp corner.
Show the first step’s working
The graph meets at \(x=8\), but it does so with a sharp corner.
Key result
\[ x=8 \]Walkthrough overview
What this question practises
This 2023 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Reading continuity, concavity, and limits from a graph.
This is Question 3(b) from the 2023 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 continuity, concavity, and limits from a graph. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.