Level 3 Differentiation Walkthrough
2022 NCEA Level 3 Differentiation Question 3(b)
2022 Paper - Reading differentiability and limits from a graph
Question
The graph below shows the function \(y=f(x)\).
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Tip to try first
Non-differentiable points often appear where the graph has a hole or a sharp corner.
Step 1
Locate the non-differentiable x-values
Reveal the explanation and working for this step.
Show the first step’s working
Look for holes, sharp corners, or jumps.
Key result
There is a hole at \(x=-4\), a corner at \(x=-1\), and another corner where the sloping segment meets the horizontal ray at \(x=1\).
Walkthrough overview
What this question practises
This 2022 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Reading differentiability, derivatives, and limits from a graph.
This is Question 3(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.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise reading differentiability, derivatives, 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.