To determine Find the gradient of the function f ( x , y ) = y − x and draw the gradient together with the level curve that passes through the point ( 2 , 1 ) . Explanation Calculation: Write the given function. f ( x , y ) = y − x (1) Partially differentiate the Equation (1) with respect to x . ∂ f ∂ x = − 1 Partially differentiate the Equation (1) with respect to y . ∂ f ∂ y = 1 Determine the gradient of the function f ( x , y ) = y − x using the equation. ∇ f = ∂ f ∂ x i + ∂ f ∂ y j Substitute –1 for ∂ f ∂ x and 1 for ∂ f ∂ y

Thomas' Calculus: Early Transcendentals (14th Edition)

14th Edition

ISBN: 9780134439020

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 14.5, Problem 1E

To determine

Find the gradient of the function f(x,y)=y−x and draw the gradient together with the level curve that passes through the point (2,1).

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Chapter 14.4, Problem 60E

Chapter 14.5, Problem 2E

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Thomas' Calculus: Early Transcendentals (14th Edition)

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