   Chapter 3.1, Problem 36E ### 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. y = x 4 − x , ( 1 , 0 )

To determine

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

Explanation

Given:

The curve is y=x4x.

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(x4x)

Apply difference rule (2),

dydx=ddx(x4)ddx(x) =ddx(x14)ddx(x)

Apply power rule (1),

dydx=(

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 