Question
Asked Sep 22, 2019
Consider the curve y = x - x*
(a) Find the slope of the tangent line to the curve at the point (1, 0)
(b) Find an equation of the tangent line in part (a)
у 3
(c) Graph the curve and the tangent line.
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Consider the curve y = x - x* (a) Find the slope of the tangent line to the curve at the point (1, 0) (b) Find an equation of the tangent line in part (a) у 3 (c) Graph the curve and the tangent line.

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check_circleExpert Solution
Step 1

Given,

y x -x3
Part A
Since, slope of the tangent line is derivative of y
dy)
y'
dx
d(x-x3)
dx
= 1 - 3x2
dy)
dx 10)
slope of the tangent line at the point (1,0)
.
- 1 - 3(1)2
=-2
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y x -x3 Part A Since, slope of the tangent line is derivative of y dy) y' dx d(x-x3) dx = 1 - 3x2 dy) dx 10) slope of the tangent line at the point (1,0) . - 1 - 3(1)2 =-2

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Step 2

Part B

So, equation of the tangent line having slope -2 and passing through the point (1,0) is

у - 0 %3D (-2)(х
— 1)
у %3 — 2х + 2
У
у+ 2х — 2
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у - 0 %3D (-2)(х — 1) у %3 — 2х + 2 У у+ 2х — 2

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Step 3

Part C

Graph of the curve and tang...

6
2
Curve
Tangent at (1,0)
|(1,0)
-2
2
--2
-4
et
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6 2 Curve Tangent at (1,0) |(1,0) -2 2 --2 -4 et

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Tagged in

Math

Calculus