Level 3 Differentiation Walkthrough
2021 NCEA Level 3 Differentiation Question 1(b)
2021 Paper
Question
The graph below shows the function \(y=f(x)\).
For the function above:
(i) Find the value(s) of \(x\) that meet the following conditions:
(ii) What is the value of \(\lim_{x\to 7} f(x)\)? State clearly if the value does not exist.
First walkthrough idea
Focus to try first
Read the shape of the graph, not just the filled dots. Limits care about where the graph approaches.
Step 1
Find where the gradient is zero
Look for a smooth point where the tangent would be horizontal.
Show the first step’s working
The curve has a smooth minimum at \(x=4\). The tangent there is horizontal.
Walkthrough overview
What this question practises
This 2021 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Reading stationary points, concavity, and limits from a graph.
This is Question 1(b) from the 2021 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 stationary points, 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
After solving the derivative condition, check the point's nature and answer the conclusion the question actually asks for.
Continue practising
- All 2021 Differentiation walkthroughs
- All AS91578 Differentiation years
- Practise more questions using this skill: Stationary points and optimisation