Explanation Given information: The function is f ( x ) = x + 1 x and the specified point is ( 4 , 5 2 ) . Formula used: The equation of a line which passes through the point ( x 1 , y 1 ) and has slope m is given by y − y 1 = m ( x − x 1 ) . This is called as point-slope form of the equation. Calculation: The derivative of the function is the slope of the tangent of its graph at any point. The given can also be written as, f ( x ) = x 1 / 2 + 1 x 1 / 2 = x 1 / 2 + x − 1 / 2 The derivative of the given function is, f ′ ( x ) = d d x f ( x ) = d d x ( x 1 / 2 + x − 1 / 2 ) Use the sum rule of differentiation , d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] . d d x ( x 1 / 2 + x − 1 / 2 ) = d d x x 1 / 2 + d d x x − 1 / 2 Use the power rule of differentiation which states that if n is a real number, then d d x ( x ) n = n x n − 1 . d d x x 1 / 2 + d d x x − 1 / 2 = ( 1 2 x 1 / 2 − 1 ) + ( − 1 2 x − 1 / 2 − 1 ) = 1 2 x − 1 / 2 − 1 2 x − 3 / 2 = 1 2 x 1 / 2 − 1 2 x 3 / 2 = 1 2 x − 1 2 x x Take 1 2 x as common factor

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.1, Problem 44E

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The slope and the equation of the tangent line of the graph of the function f at the specified point.

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Chapter 3.1, Problem 43E

Chapter 3.1, Problem 45E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The slope and the equation of the tangent line of the graph of the function f at the specified point.

Solution Summary: The author explains the function's derivative, which is the slope of the tangent of its graph at any point.

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The slope and the equation of the tangent line of the graph of the function f at the specified point.

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Chapter 3 Solutions