Explanation Given: Function f ( x ) = ( 2 x − 3 ) 3 Formula Used: Equation of line using slope-point form is given as ( y − y 1 ) = m ( x − x 1 ) where ( x 1 , y 1 ) is point of line and m is the slope of the line Calculation: Function is given as f ( x ) = ( 2 x − 3 ) 3 . Let us find the point on graph where tangent is drawn Put x = 0 in f ( x ) , we get f ( 0 ) = ( 2 ( 0 ) − 3 ) 3 f ( 0 ) = ( − 3 ) 3 f ( 0 ) = − 27 Also, slope of the line is calculated by taking the derivative of the function f ′ ( x ) = d d x ( 2 x − 3 ) 3 Let u = 2 x − 3 and f = u 3 Thus, using chain rule of derivative, we have f ′ ( x ) = d f d u . d u d x f ′ ( x ) = d d u ( u 3 ) To determine (b) To find the equation of tangent line to the graph of f ( x ) = ( 2 x − 3 ) 3 at the point at which x = 2 .

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 3.3, Problem 34P

To determine

(a)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=0.

To determine

(b)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=2.

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Chapter 3.3, Problem 33P

Chapter 3.3, Problem 35P

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(a) To find the equation of tangent line to the graph of f ( x ) = ( 2 x − 3 ) 3 at the point at which x = 0 .

Solution Summary: The author explains how to find the equation of tangent line to the graph of f(x) = 54x-27.

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(a)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=0.

(b)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=2.

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Chapter 3 Solutions

(a) To find the equation of tangent line to the graph of f ( x ) = ( 2 x − 3 ) 3 at the point at which x = 0 .

Solution Summary: The author explains how to find the equation of tangent line to the graph of f(x) = 54x-27.

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(a) To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=0.

(b) To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=2.

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Chapter 3 Solutions

(a)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=0.

(b)

To find the equation of tangent line to the graph of f(x)=(2x−3)3 at the point at which x=2.