   Chapter 3.3, Problem 25E ### 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

# (a) Find an equation of the tangent line to the curve y = 2x sin x at the point (π/2, π).(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

(a)

To determine

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

Explanation

Given:

The equation of the curve is y=2xsinx and the point is (π2,π).

Derivative rules:

(1) Constant Multiple Rule: ddx[cf(x)]=cddxf(x)

(2) Power Rule: ddx(xn)=nxn1

(3) Product Rule: ddx(f(x)g(x))=f(x)ddx(g(x))+g(x)ddx(f(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(2xsinx)

Apply the product rule (3),

dydx=2xddx[sinx]+sinxddx[2x]

Apply the constant multiple rule (1),

dydx=2xddx[sinx]+

(b)

To determine

To sketch: The given curve and the tangent line at the given point (π2,π).

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