QCAA Maths Methods Differential Calculus Mini Test 7
External Assessment Paper 1 — Technology-free
Number of marks: 11
Perusal time: 1 minute
Writing time: 16 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
A tangent is drawn at the point \((1, e)\) on the graph of the function \(y = e^{2-x}\) as shown.

Determine the area of the shaded triangle.
A function is defined as \(f(x) = x(\ln(x))^2, x > 0\).
The graph of the function is shown and has a local maximum at point \(A\) and a global minimum at point \(B\).
The derivative of the function is given by \(f'(x) = 2 \ln(x) + (\ln(x))^2, x > 0\).

a) Verify that there is a stationary point at \(x = 1\). [2 marks]
b) Determine the coordinates of \(A\). [3 marks]
c) The graph of the function has a point of inflection at \(x = e^p\).
Determine \(p\). [2 marks]
END OF PAPER