Question: Let D be a disk in R 2 . This exercise shows that if Vf(x, y) = 0 for all (x, y) in D, then

Let D be a disk in R². This exercise shows that if

Vf(x, y) = 0 for all (x, y) in D, then f is constant. Consider points P = (a,b), Q = (c,d), and R = (c, b) as

Vf(x, y) = 0 for all (x, y) in D, then f is constant. Consider points P = (a,b), Q = (c,d), and R = (c, b) as in Figure 16. (a) Use single-variable calculus to show that f is constant along the segments PR and RQ. (b) Conclude that f(P) = f(Q) for any two points P, Q = D. Q = (c,d) P = (a, b) R = (c, b) Disk D -X

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