Problem

(a) The curve $ y = x/(1 + x^2) $ is called a ser…

02:59

Problem 35 Medium Difficulty

(a) The curve $ y' = 1/(1 + x^2) $ is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point $ (-1, \frac {1}{2}).
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

Answer

(a) $y=\frac{1}{2} x+1$
(b) Please see the graph of this amazing witch riding on her broom

More Answers

01:12

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

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Video Transcript

it's clear. So a new ranger So we're given why is equal to one over one plus x square. So we need to find the derivative of this and we're gonna use the quotient role, which gives us one plus x square. Comes the derivative of one minus one times the derivative of one plus X square all over one plus x square square. And this gives us negative to X over one plus x square square. No, we plug in to find a slope and we get 1/2 when we substitute the equation for why minus 12. 1/2 is equal to em. Times X plus one we get Why minus one have this equal to 1/2 times X plus one. And this becomes why is equal to when have X plus one. And for part B, we're gonna draw our graph. You don't look like this in our tangent line in red

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham