Tangent lines Find an equation of the line | Ch 10.4 - 71E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 71E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Problem 71E

Tangent lines Find an equation of the line tangent to the following curves at the given point.

Step-by-Step Solution:

Solution 71E

Step 1:

Tangent lines Find an equation of the line tangent to the following curves at the given point.

Step 2 :

Let us differentiate the given equation in terms of x

$\frac{d}{dx}\left({{y}^{2}-\frac{{x}^{2}}{64}}\right)=\frac{d}{dx}(1)$

$\Rightarrow{}\ 2y\frac{dy}{dx}-\frac{2x\ }{64}=0$

$\Rightarrow{}2y\frac{dy}{dx}=\frac{2x}{64}$

$\Rightarrow{}y'=\frac{x}{64y}$ $\$

Now lets substitute the given points $\left({6,-\frac{5}{4}}\right)$ into $\Rightarrow{}y'=\frac{x}{64y}$ to get the slope m

$\Rightarrow{}m=y'=\frac{6}{64\times{}-\frac{5}{4}}=-\frac{3}{40}$

Step 3:

The equation of the tangent line is

$y=mx+b$

For this we have to find the value of b.

For this we will substitute $\left({6,-\frac{5}{4}}\right)$ in $y=mx+b$

Therefore $y=mx+b\Rightarrow{}\ \ \ \frac{-5}{4}=\frac{-3}{40}x+b$

Therefore $b=\frac{-4}{5}$

Step 4 of 5

Chapter 10.4, Problem 71E is Solved

Step 5 of 5

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Tangent lines Find an equation of the line tangent to the following curves at the given point.” is broken down into a number of easy to follow steps, and 17 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Tangent, line, Find, given, equation. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 71E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 71E from 10.4 chapter was answered, more than 254 students have viewed the full step-by-step answer.