Explanation Given information: The curve: y = x / ( x + 1 ) and the point ( 1 , 2 ) Calculation: Let f ( x ) = x x + 1 . The derivative of f ( x ) is obtained using the Quotient Rule f ' ( x ) = ( x + 1 ) ( x ) ' − x ( x + 1 ) ' ( x + 1 ) 2 = x + 1 − x ( x + 1 ) 2 = 1 ( x + 1 ) 2 So the slope of the tangent line at the point, say, ( a , a a + 1 ) is y − a a + 1 = f ' ( a ) ( x − a ) y − a a + 1 = 1 ( a + 1 ) 2 ( x − a ) ( ∗ ) Where a is any real number. The tangent line passes through the point ( 1 , 2 ) is the coordinates of that point satisfy the derived equation of that tangent line. Substituting the coordinates of the point into Eq

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ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.4, Problem 59E

To determine

To find: the number oftangent lines to the curve y=x/(x+1) which pass through the point (1,2). Also find points at which tangent lines touch the curve.

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Chapter 3.4, Problem 58E

Chapter 3.4, Problem 60E

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Chapter 3 Solutions

Biocalculus

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the number oftangent lines to the curve y = x / ( x + 1 ) which pass through the point ( 1 , 2 ) . Also find points at which tangent lines touch the curve.

Solution Summary: The author calculates the derivative of f(x) using the Quotient Rule.

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To find: the number oftangent lines to the curve y=x/(x+1) which pass through the point (1,2). Also find points at which tangent lines touch the curve.

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Chapter 3 Solutions