Level 3 Differentiation Walkthrough
2025 NCEA Level 3 Differentiation Question 1(b)
2025 Paper
Question
The temperature of an oven is given by the formula \[ C=\frac{60}{\sqrt{t}}+5\sqrt{t}+15, \] where \(C\) is the temperature of the oven, in \(^\circ\text{C}\), and \(t\) is the time, in minutes, after the oven has been switched off.
Find the rate of change of the temperature of the oven \(4\) minutes after the oven was switched off.
You must use calculus and show any derivatives that you need to find when solving this problem.
First walkthrough idea
Hint to try first
Rewrite the square roots as powers first so the power rule is easier to use.
Step 1
Rewrite in power form
\(\frac{1}{\sqrt{t}}=t^{-1/2}\) and \(\sqrt{t}=t^{1/2}\).
Show the first step’s working
\(\frac{1}{\sqrt{t}}=t^{-1/2}\) and \(\sqrt{t}=t^{1/2}\).
Key result
\[ 60t^{-1/2}+5t^{1/2}+15 \]Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Rewriting in power form and finding a rate of change.
This is Question 1(b) from the 2025 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 rewriting in power form and finding a rate of change. 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.