Problem

Find an equation of the tangent line to the given…

01:41

Problem 31 Easy Difficulty

Find an equation of the tangent line to the given curve at the specified point.

$ y = \frac {x^2 - 1}{x^2 + x + 1}, (1,0) $

Name: find an equation of the tangent line to the given curve at the specified point y frac x2 1x2 x 1 10
Uploaded: 2019-12-02
Duration: 1 min 52 s
Channel: Numerade
Description: Find an equation of the tangent line to the given curve at the specified point. $ y = \frac {x^2 - 1}{x^2 + x + 1}, (1,0) $

Answer

$y=\frac{2}{3} x-\frac{2}{3}$

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Video Transcript

Hey, it's from someone. You rain here, so we have. Why is equal to X square minus one all over X square plus X plus one. We're gonna use the quotient role to find the derivative when we get X square minus one The derivative X square plus X plus one minus X square minus one and the derivative of X square plus X plus one This is all over X square plus X plus one square. When we simplify this, we get X square. It was for X plus one while over at square, less X plus one square. So to find a slope of the tangent line at one comma zero we're gonna plug in X is equal to one into our derivative when we get 2/3. So we're gonna create a line Why is equal to 2/3 X minus one plus zero? This becomes equal to two birds. X minus 2/3

Clarissa N.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Problem