Mathematical Methods — Question 16

ANSWER

A possible function is $y=2\cos\left(\frac32x\right)$.

Worked solution

The provided functions are a sine and a cosine function, both with negative amplitudes and the same period. Therefore, the smooth line is $y'=-a\sin(bx)$ and the dotted line is $y''=-A\cos(bx)$, with $a=3$ and $A=4.5$. Therefore, the primary function must be a cosine function with the same period, e.g. $$y=2\cos\left(\frac32x\right).$$

correctly identifies the smooth curve as the first derivative

[1 mark]

provides mathematical reasoning for sketch

[1 mark]

sketches the function

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.