Suppose you're climbing a hill whose shape is given by the equation z = 1000 – 0.003x² – 0.005y?, where the positive x-axis represents east, the positive y-axis represents north, and z represents the upward direction. If you are standing at a point with coordinates (60,45), in what direction is the slope of the hill largest?

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Directional Derivatives and the Gradient Vector
Suppose you're climbing a hill whose shape is given by the equation z
1000 – 0.003x² –
0.005y2, where the positive x-axis represents east, the positive y-axis represents north, and z
represents the upward direction. If you are standing at a point with coordinates (60,45), in
what direction is the slope of the hill largest?
Transcribed Image Text:Directional Derivatives and the Gradient Vector Suppose you're climbing a hill whose shape is given by the equation z 1000 – 0.003x² – 0.005y2, where the positive x-axis represents east, the positive y-axis represents north, and z represents the upward direction. If you are standing at a point with coordinates (60,45), in what direction is the slope of the hill largest?
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