Explanation Given: The function, f ( x ) = x 2 + 5 x + 5 Concept Used: Slope of the tangent line of a function f ( x ) at any point x = c is given by the first derivative at that point. That is the slope of tangent line at x = c is given by f ′ ( c ) . The point-slope form of the line passing through the point ( x 1 , y 1 ) and having slope m is given by y − y 1 = m ( x − x 1 ) . Power rule of derivatives, d d x ( x n ) = n x n − 1 Quotient rule of derivatives, ( u v ) ′ = v ⋅ u ' − u ⋅ v ' v 2 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: Consider the function, f ( x ) = x 2 + 5 x + 5 In order to find the equation of tangent line, first we find the slope of tangent line by finding the first derivative at the specified point. So, using the quotient rule and power rule of derivatives, the first derivative of the function can be found as, f ' ( x ) = ( x + 5 ) ⋅ d d x ( x 2 + 5 ) − ( x 2 + 5 ) ⋅ d d x ( x + 5 ) ( x + 5 ) 2 = ( x + 5 ) ⋅ ( 2 x + 0 ) − ( x 2 + 5 ) ⋅ ( 1 + 0 ) ( x + 5 ) 2 = 2 x ( x + 5 ) − ( x 2

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.2, Problem 31PS

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The equation of the tangent line to the graph of f(x)=x2+5x+5 at x=1 .

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Chapter 3.2, Problem 30PS

Chapter 3.2, Problem 32PS

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Chapter 3 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The equation of the tangent line to the graph of f ( x ) = x 2 + 5 x + 5 at x = 1 .

Solution Summary: The author explains that the slope of the tangent line of a function f(x) is given by the first derivative at the specified point.

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The equation of the tangent line to the graph of f(x)=x2+5x+5 at x=1 .

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