Figure 4 shows the contour map of a function (x, y) together with a path r(t) in the counterclockwise direction. The points r(1), r(2), and

Figure 4 shows the contour map of a function ƒ(x, y) together with a path r(t) in the counterclockwise direction. The points r(1), r(2), and r(3) are indicated on the path. Let g(t) = ƒ (r(t)). Which of statements (i)–(iv) are true? Explain.

(i) g'(1) > 0.
(ii) g(t) has a local minimum for some 1 ≤ t ≤ 2.
(iii) g'(2) = 0.
(iv) g'(3) = 0.

r(1) r(1) 0 0 -2 -6 -2 r(2) -4 r(3) 4 2