   Chapter 3.1, Problem 35E

Chapter
Section
Textbook Problem

Find an equation of the tangent line to the curve at the given point. y = x + 2 x , ( 2 , 3 )

To determine

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

Explanation

Given:

The curve y=x+2x.

The point is (2,3).

Derivative rules:

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

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

(3) Sum 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(x+2x)

Apply sum rule (3) and constant multiple rule (1),

dydx=ddx(x)+ddx(2x)=ddx(x)+ddx(2x1)=ddx(x)+2

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