Explanation Given information: The function is f ( x ) = ( x 2 + 6 ) ( x − 5 ) and the slope of tangent line is − 2 . Formula used : The product rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Calculation: The derivative of the given function gives the slope of the tangent line. Apply the product rule of differentiation for the given function to get the derivative function f ′ ( x ) . f ′ ( x ) = d d x [ ( x 2 + 6 ) ( x − 5 ) ] = ( x 2 + 6 ) ⋅ d d x ( x − 5 ) + ( x − 5 ) ⋅ d d x ( x 2 + 6 ) = ( x 2 + 6 ) ⋅ ( 1 ) + ( x − 5 ) ⋅ ( 2 x ) = x 2 + 6 + 2 x 2 − 10 x ( Apply distributive property ) Further solve the above equation for f ′ ( x ) . f ′ ( x ) = 3 x 2 − 10 x + 6 ( Combine like terms ) (1) The slope of tangent line is, m = f ′ ( x ) (2) The slope of tangent line is − 2 . Substitute − 2 for m in equation (2), f ′ ( x ) = − 2 Substitute 3 x 2 − 10 x + 6 for f ′ ( x ) from equation (1) to the above equation and solve for x

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ISBN: 9781305041264

Author: Tan

Publisher: CENGAGE C

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Chapter 3.2, Problem 49E

To determine

To find: The points on the graph of given function f(x) when the slope of tangent line is −2 .

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Chapter 3.2, Problem 48E

Chapter 3.2, Problem 50E

Chapter 3 Solutions

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The points on the graph of given function f ( x ) when the slope of tangent line is − 2 .

Solution Summary: The author explains that the derivative of the given function gives the slope of tangent line.

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To find: The points on the graph of given function f(x) when the slope of tangent line is −2 .

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Chapter 3 Solutions