Explanation Formula used: Equation of a tangent line is, y − y 1 = m ( x − x 1 ) (1) Given information: The given equation is y 2 − x 2 = 16 and indicated point is ( 2 , 2 5 ) . Calculation: Differentiate the given equation with respect to x and simplify, d d x ( y 2 − x 2 ) = d d x ( 16 ) d d x ( y 2 ) − d d x ( x 2 ) = d d x ( 16 ) 2 y d y d x − 2 x = 0 ( d d x ( x n ) = n x n − 1 ) 2 y d y d x = 2 x ( Add 2 x in each side ) Further simplify the above expression, d y d x = 2 x 2 y ( Divide by 2 y in each side ) = x y Now, calculate the slope of a tangent line by using the given indicated points

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.6, Problem 32E

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The equation of a tangent line of the given function at the indicated point.

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Chapter 3.6, Problem 31E

Chapter 3.6, Problem 33E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The equation of a tangent line of the given function at the indicated point.

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