The graph of f has a minimum at $\mathrm{P}(4,8)$ and a maximum at $\mathrm{Q}(12,16) $.
1. a. Find the value of c .
b. Show that $k=\frac{\pi}{8} $.
c. Find the value of a .
The graph of g is obtained from the graph of f by a translation of $\binom{d}{0}$ .
The minimum point on the graph of g has coordinates (6.5,8) .
2. a. Write down the value of d .
b. Find g(x) .
The graph of g changes from concave-up to concave-down when $x=\nu$ .
3. a. Find $\nu$ .
b. Hence, or otherwise, find the maximum positive rate of change of g .≈
