The surface S is given by f(x,y) = 9-x^2-y^2
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We know the directional derivative of z=f(x,y) at (1,1) in the direction of (-1,-6) is the rate of change of z=f(x,y) at (1,1) in the direction of (-1,-6), which is
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Question 1: Why is this directional derivative positive?
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Perhaps moving the black vector in the xy-plane so that it starts at the purple point might help.
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Answer:
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Homework: Compare this Desmos to Desmos 14.3 on Partial Derivatives.
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Question 2: From (1,1), can we head on a different direction to get a larger directional derivative?
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All Done .
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Ignore this set-up folder (colors)
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