QCAA Maths Methods Differential Calculus Mini Test 9
External Assessment Paper 1 — Technology-free
Number of marks: 10
Perusal time: 1 minute
Writing time: 15 minutes
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
A horizontal point of inflection is a point of inflection that is also a stationary point.
Determine the value/s of \(k\) for which the graph of \( f(x) = \frac{\ln(x)}{k} - \frac{kx}{x+1} \) has only one horizontal point of inflection.
Consider the following graph of \(f(x)\).
Identify the graph of the second derivative \(f''(x)\) from the graphs in Diagram 1, Diagram 2 and Diagram 3.
Justify your decisions using mathematical reasoning.
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