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# Answer: Vertical tangent lines If a function f is ISBN: 9780321570567 2

## Solution for problem 64AE Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 64AE

Vertical tangent lines? If a function f is continuous at a and , then the curve y= f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions. Graph the following curves and determine the location of any vertical tangent lines. a.? x2 + y2 = 9 b.? x2 + y2 + 2x = 0

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SOLUTION If a function f is continuous at a and lim|f (x)| = , then the curve y= f(x) has a xa vertical tangent line at a and the equation of the tangent line is x = a STEP 1 2 2 (a). Given the function x +y = 9 2 We can write this function as y =± 9x Now,let’s differentiate this function y, 2x x Therefore y = 2 9x = 9x2 Now let us take the left hand and the right hand limits. lim|f(x)| = lim| x |= x3 x3 9x2 lim |f(x)| = lim | x 2|= x3 x3 9x Therefore,we have lim|f (x)| = lim |f(x)| = x3 x3 Thus the given function has vertical tangent lines at x=3 and x=-3 STEP 2 (b). Given the function x +y +2x = 0 We can write this function as y =± x 2x 2 Now,let’s differentiate this function y, Therefore y = 2x2 = x1 = (x+1) 2x 2x x 2x x 2x Now let us take the left hand and the right hand limits. lim|f(x)| = lim| x+1 |= x0 x0 x 2x lim |f(x)| = lim | x+1 |= x2 x2 x 2x Therefore,we have lim|x0 (x)| =x2 |f(x)| = Thus the given function has vertical tangent lines at x=0 and x=-2

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##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Vertical tangent lines? If a function f is continuous at a and , then the curve y= f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions. Graph the following curves and determine the location of any vertical tangent lines. a.? x2 + y2 = 9 b.? x2 + y2 + 2x = 0” is broken down into a number of easy to follow steps, and 88 words. Since the solution to 64AE from 3.1 chapter was answered, more than 358 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 64AE from chapter: 3.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Tangent, vertical, Lines, line, exercises. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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Answer: Vertical tangent lines If a function f is