   Chapter 2.7, Problem 5E ### 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 = 4x – 3x2, (2, –4)

To determine

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

Explanation

Given:

The equation of the curve is y=4x3x2.

The curve passing through the point (2,4).

Formula used:

The slope of the tangent curve y=f(x) at the point P(a,f(a)) is,

m=limxaf(x)f(a)xa (1)

The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is,

yf(a)=f(a)(xa) (2)

Calculation:

Obtain the slope of the tangent line to the curve at the point (2,4).

Substitute a=2 and f(a)=4 in equation (1),

m=limx2f(x)f(2)x1=limx2(4x3x2)(4)x2=limx23x2+4x+4x2=limx2(3x24x4)x2

The factors of (3x24x4) is (3x+2) and (x2)

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