Explanation Given: The given equation is x 3 + y 3 = y + 21 at ( 3 , − 2 ) Concept Used: To find an equation of the tangent line to the graph of an equation y = f ( x ) at the a point ( a , b ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) Now, the equation of the tangent line to the graph of the equation is y = m x + c Put ( a , b ) coordinate in y = m x + c to find the value of c Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where u is a differentiable function at x and f is a differentiable function at u ( x ) Power rule of differentiation formula d d x x n = n x n − 1 Calculation: To find an equation of the tangent line to the graph of x 3 + y 3 = y + 21 at ( 3 , − 2 ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) For that differentiate both side of the equation with respect to x as x 3 + y 3 = y + 21 d d x ( x 3 + y 3 ) = d d x ( y + 21 ) d d x x 3 + d d x y 3 = d y d x Now, above can be simplified using chain rule of differentiation, as d d x x 3 + d d x y 3

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 3.6, Problem 26PS

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To find an equation of the tangent line to the graph of given equation x3+y3=y+21 at (3,−2) .

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Chapter 3.6, Problem 25PS

Chapter 3.6, Problem 27PS

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Chapter 3 Solutions

Calculus

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To find an equation of the tangent line to the graph of given equation x 3 + y 3 = y + 21 at ( 3 , − 2 ) .

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To find an equation of the tangent line to the graph of given equation x3+y3=y+21 at (3,−2) .

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Chapter 3 Solutions