Functions question?

Question

The function f is defined for the domain -3 f(x) = 9 (x - 1/3)^2 - 11

(i) Find the range of f.

(ii) State the coordinates and nature of the turning point of
(a) the curve y = f(x)
(b) the curve y = I f(x) I

Answer 1

i. The maximum must be at f(-3) = 89. The minimum will be at f(1/3) = -11. The range is (-11,89).

iia. It is the minimum of a parabola at (1/3, -11). This is confirmed by differentiating the function and equating to zero.
f' = 18x - 6 = 0 -> x = 1/3

iib. There are three turning points. One is a parabola maximum at (1/3,11). The other two are minima at f(0) = 0 and at x = -0.772 and 1.44.