Explanation Given information: The function, y = x 2 ( 1 − sin x ) Concept used: Product rule of derivatives, d d x ( f ( x ) ⋅ g ( x ) ) = f ( x ) ⋅ g ' ( x ) + g ( x ) ⋅ f ' ( x ) Derivative of any constant is zero. Calculation: The slope of the tangent line at any point on the curve, is given by the first derivative of the function at that point. So in order to find the equation of the tangent line, first we will find the slope of the tangent line by finding the derivative. So using the product rule, we get y ' = d d x ( x 2 ( 1 − sin x ) ) = x 2 ⋅ ( 1 − sin x ) ' + ( 1 − sin x ) ⋅ ( x 2 ) ' Using product rule = x 2 ⋅ ( 0 − cos x ) + ( 1 − sin x ) ⋅ ( 2 x ) Simiplify = − x 2 cos x + 2 x − 2 x sin x So at the point x = 3 π 2 , slope of the tangent line is y ' = − ( 3 π 2 ) 2 cos ( 3 π 2 ) + 2 ( 3 π 2 ) − 2 ( 3 π 2 ) sin ( 3 π 2 )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 3.6, Problem 33E

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To find the equation of the tangent line at the point x=3π2

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Chapter 3.6, Problem 32E

Chapter 3.6, Problem 34E

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Tangent lines are drawn to the curve y = -x2 − 2 from the point (0, 2). Find the points at which the tangent lines touch the curve. Also illustrate with a diagram.

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Chapter 3 Solutions

Calculus - Standalone book

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To find the equation of the tangent line at the point x = 3 π 2

Solution Summary: The author explains how to find the equation of the tangent line at any point on the curve, using the product rule.

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To find the equation of the tangent line at the point x=3π2

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