Explanation Given function is, y = - 8 x + 1 Given point is, x = 3 . Substituting x = 3 in the above function, y = - 8 3 + 1 y = - 24 + 1 y = - 25 y = - 5 x , y = 3 , - 5 The equation of the tangent line to the graph of the function at the value of x is, y - y 1 = m ( x - x 1 ) x 1 , y 1 = 3 , - 5 m = s l o p e m = d y d x Where, y = - 8 x + 1 can be written as, y = - 8 x + 1 1 2 d y d x can be determined by the following rule, Chain rule states that, If y is a function of u , say y = f ( u ) , and if u is a function of x , say u = g ( x ) , then y = f u = f [ g x ] , and d y d x = d y d u · d u d x Based on the above chain rule, Let, u = 8 x + 1 1 2 . So the function y = - 8 x + 1 1 2 can be written as, y = - u d y d u = - d u d u d y d u = - 1 d u d x = d 8 x + 1 1 2 d x According to the power rule, d u d x = 1 2 8 x + 1 1 2 - 1 8 x 1 - 1 + 0 d u d x = 1 2 8 x + 1 - 1 2 8 d u d x = 1 2 8 x + 1 - 1 2 8 d u d x = 8 2 8 x + 1 -

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 4.CR, Problem 76CR

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The equation of the tangent line to the graph of the function y=-8x+1 at x=3.

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The equation of the tangent line to the graph of the function y = - 8 x + 1 at x = 3 .

Solution Summary: The author explains how the equation of the tangent line to the graph of a function is y=-sqrt8x+1.

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The equation of the tangent line to the graph of the function y=-8x+1 at x=3.

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The equation of the tangent line to the graph of the function y = - 8 x + 1 at x = 3 .

Solution Summary: The author explains how the equation of the tangent line to the graph of a function is y=-sqrt8x+1.

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To find: The equation of the tangent line to the graph of the function y=-8x+1 at x=3.

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Chapter 4 Solutions

To find:

The equation of the tangent line to the graph of the function y=-8x+1 at x=3.