Dear ZaiDancerz,
Try to write something in your test.
Typically, a problem on maxima and minima will ask you to
show a result (e.g. area, volume, cost, etc. Then you will proceed
to find its maximum or minimum.
Nevermind if you can't show the result. Just carry out
differentiation on the result and find the stationary value(s).
Then carry out differentiation again to determine the nature. You
will score some marks by doing these.
Example:
(a) Show that the volume V of the cuboid is given by V = 360
x^2 - 6 x^3.
(b) Find the value of x for which V is stationary.
(c) Determine the nature of the stationary point and hence
find its value.
You can proceed to answer (b) and (c), skipping
(a) if you are stuck.
For (b), we first differentiate V with respect to x,
i.e.,
dV / dx = 720 x - 18 x^2.
For stationary V, equate dV / dx to zero and solve for x,
i.e.,
720 x - 18 x^2 = 0
18 x (40 - x) = 0
x = 40.
For (c), we first differentiate dV / dx with respect to
x, i.e.,
d^2 V / dx^2 = 720 - 36 x.
When x = 40, d^2 V / dx^2 = 720 - 36(40) <
0, so x = 40 gives maximum V.
When x = 40, maximum V = 360 (40^2) - 6 (40^3) = 192
000.
Good luck!
Cheers,
Wen Shih