AS 91578 · 2023 paper · gradient of normal, turning points, a proof
Question 3(b)(iii) Achieved
Practises Reading a graph: differentiability, f′ = 0, and limits
A log chain rule, three readings off a drawn graph, a parametric normal on a Ferris wheel, stationary points of a reciprocal pair, and a catenary to verify by substitution.
What is the value of limx → 6 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.
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1 What height does the graph approach from the left of x = 6? And from the right?
From the left, the curve rises to 2 (the filled dot). From the right, the line starts from 5 (the open circle). -
2 Do the two sides agree?
No: 2 and 5. So the limit does not exist, even though f(6) = 2 is defined.
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 2023 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.