   Chapter 3.1, Problem 40E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = x − x , ( 1 , 0 )

To determine

To find: The equation of the tangent line to the curve and to sketch the given curve and the tangent line at the given point.

Explanation

Given:

The equation of the curve is y=xx and the point is (1,0).

Derivative rules:

(1) Power rule: ddx(xn)=nxn1

(2) Difference rule:ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

where, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

The derivative of y is dydx , which is obtained as follows.

dydx=ddx(y) =ddx(xx) =ddx(xx12)

Apply the difference rule (2),

dydx=ddx(x)ddx(x12)

Simplify the expression using the power rule (1),

dydx=(1x11)(12x121)  =(1x0

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