Level 3 Differentiation Walkthrough
2024 NCEA Level 3 Differentiation Question 3(b)
2024 Paper
Question
The graph below shows the function \(y=f(x)\).
(i) Find the value(s) of \(x\) where \(f(x)\) is continuous but not differentiable.
(ii) Find the value(s) of \(x\) where \(f'(x)=0\).
(iii) Find \(\lim\limits_{x\to -1}f(x)\), or state clearly if it does not exist.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Hint to try first
Continuous but not differentiable usually means a corner or cusp, not a jump.
Step 1
Find where the graph is joined but has a sharp change
The graph is connected at \(x=5\), but the gradient changes suddenly there.
Show the first step’s working
The graph is connected at \(x=5\), but the gradient changes suddenly there.
Key result
\[ x=5 \]Walkthrough overview
What this question practises
This 2024 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Reading continuity, differentiability, and limits from a graph.
This is Question 3(b) from the 2024 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.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise reading continuity, differentiability, 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.