AS 91578 · 2025 paper · the graph, related rates, rectangle optimisation
Question 3(a)(iii) Achieved
Practises Reading a graph: differentiability, f′ = 0, and limits
Reading differentiability, stationary points and a limit straight off a drawn graph, then a log quotient, a related-rates sphere, a parametric gradient, and a rectangle inscribed in a curve.
What is the value of limx → −2 f(x)? State clearly if the value does not exist.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
-
1 What height does the graph approach as x comes towards −2 from the left? And from the right?
From the left, the curve comes down towards y = 2. From the right, the line starts from y = 2. -
2 Does the filled dot at (−2, 7) change the answer?
No. A limit is about the heights close to x = −2, not the value at x = −2. The two sides agree on 2.
What the marker wanted
- Achieved Two of the three answers to (i), (ii) and (iii) correct.
The schedule marks (i), (ii) and (iii) together as one Achieved item: any two of the three correct earns it.
In our words, from NZQA’s 2025 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.