Level 3 Differentiation Walkthrough
2021 NCEA Level 3 Differentiation Question 2(e)
2021 Paper
Question
The graph below shows the curve
and the tangent to the curve at point \(P\). The tangent passes through the point \((-2,1)\).
Find the coordinates of point \(P\).
You must use calculus and show any derivatives that you need to find when solving this problem.
First walkthrough idea
Focus to try first
At point \(P\), the derivative of the curve must match the gradient of the tangent line through \((-2,1)\).
Step 1
Differentiate the curve
Rewrite the square root as a power if that helps.
Show the first step’s working
Walkthrough overview
What this question practises
This 2021 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Tangent geometry on \(y=\sqrt{2x-4}\).
This is Question 2(e) from the 2021 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 tangent geometry on \(y=\sqrt{2x-4}\). Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Use the derivative for the gradient and the original curve for the point before forming the tangent equation.