Let f be differentiable and grad f(2, 1) = 3i + 4j .You want to see if (2, 1) is a

Chapter 15, Problem 46

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Let f be differentiable and grad f(2, 1) = 3i + 4j .You want to see if (2, 1) is a candidate for the maximumand minimum values of f subject to a constraint satisfiedby the point (2, 1).(a) Show (2, 1) is not a candidate if the constraint isx2 + y2 = 5.(b) Show (2, 1) is a candidate if the constraint is (x 5)2 + (y + 3)2 = 25. From a sketch of the contoursfor f near (2, 1) and the constraint, decide whether(2, 1) is a candidate for a maximum or minimum.(c) Do the same as part (b), but using the constraint(x + 1)2 + (y 5)2 = 25.