Explanation Given: The point P = ( 2 , 1 ) on the curve y 3 + 3 x y = 7 . Formula used: The formula of linearization L ( x ) , centered at x = a is: L ( x ) = f ′ ( a ) ( x − a ) + f ( a ) Calculation: The curve is y 3 + 3 x y = 7 . Differentiate the function with respect to x . 3 y 3 − 1 d y d x + 3 [ x d d x y + y d d x x ] = 0 3 y 2 d y d x + 3 [ x d y d x + y ] = 0 3 y 2 d y d x + 3 x d y d x + 3 y = 0 Simplify the above equation. 3 y 2 d y d x + 3 x d y d x = − 3 y ( 3 y 2 + 3 x ) d y d x = − 3 y d y d x = − 3 y 3 y 2 + 3 x d y d x = − y y 2 + x Now, find the value of d y d x at point P = ( 2 , 1 )

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 67E

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Find dydx. Show that the linearization at P is L(x)=−13x+53. Use L(x) to estimate the y− coordinate of the point on the curve where x=2.1.

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Chapter 4.1, Problem 66E

Chapter 4.1, Problem 68E

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Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find d y d x . Show that the linearization at P is L ( x ) = − 1 3 x + 5 3 . Use L ( x ) to estimate the y − coordinate of the point on the curve where x = 2.1 .

Solution Summary: The author explains that the linearization at P is L(x).

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Find dydx. Show that the linearization at P is L(x)=−13x+53. Use L(x) to estimate the y− coordinate of the point on the curve where x=2.1.

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Chapter 4 Solutions