AS 91578 · 2024 paper · sec, graph, cone, triangle area
Question 3(b)(ii) Achieved
Practises Reading a graph: differentiability, f′ = 0, and limits
A product with sec, three readings off a drawn graph (continuity, stationary points, a limit), stationary points of a rational function, a related-rates cone, and an optimisation that has to be proved to a given exact value.
For the function above, find the value(s) of x where f'(x) = 0.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 Where is the tangent horizontal at a single point?
At the top of the curve, x = 1. -
2 Is there a stretch where the graph is flat?
Yes: the line at y = −1 from x = 3 to x = 5. Its gradient is 0 all along, but not at either end, where there is a jump (x = 3) and a corner (x = 5). So 3 < x < 5.
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 2024 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.