Figure 4 shows the contour map of a function (x, y) together with a path r(t) in
Question:
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.
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