Level 3 Differentiation Walkthrough
2024 NCEA Level 3 Differentiation Question 1(c)
2024 Paper
Question
For the function below, find the range of values of \(x\) for which the function is decreasing. \[ y=3(2x-7)^2+60\ln x+12,\qquad x>0 \]
You must use calculus and show any derivatives that you need to find when solving this problem.
First walkthrough idea
Focus to try first
differentiating first, then solving \(\frac{dy}{dx}<0\) to locate the interval where the graph is falling.
Step 1
Find the derivative
That matches the term-by-term derivative.
Show the first step’s working
That matches the term-by-term derivative.
Key result
Walkthrough overview
What this question practises
This 2024 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Differentiating, solving \(f'(x)=0\), and finding where a function is decreasing.
This is Question 1(c) from the 2024 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 differentiating, solving \(f'(x)=0\), and finding where a function is decreasing. 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.