Explanation Given information: The equation is, y = 4 − x 2 (1) The point is ( 1 , 3 ) . Formula used: The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, h ′ ( x ) = d d x g [ f ( x ) ] = g ′ [ f ( x ) ] f ′ ( x ) The formula to calculate the slope of the tangent is, m = d y d x (2) The formula to calculate the equation of line of tangent is, y − y 1 = m ( x − x 1 ) (3) Calculation: Differentiate both sides of the equation (1) with respect to x by chain rule. d y d x = d d x ( 4 − x 2 ) 1 / 2 = 1 2 ( 4 − x 2 ) 1 2 − 1 d d x ( 4 − x 2 ) = 1 2 ( 4 − x 2 ) − 1 2 ( − 2 x ) = − x ( 4 − x 2 ) − 1 / 2 Substitute − x ( 4 − x 2 ) − 1 / 2 for d y d x in equation (2) to calculate the slope m . m = − x ( 4 − x 2 ) − 1 / 2 Substitute 1 for x from the given point ( 1 , 3 ) in the above equation to calculate m

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3, Problem 49RE

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To find: The equation of the tangent line.

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Chapter 3, Problem 47RE

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The equation of the tangent line.

Solution Summary: The author explains the equation of the tangent line and the formula to calculate the differential of a function.

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Chapter 3 Solutions