   Chapter 2.4, Problem 33E

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# For what values of x does the graph of f ( x ) = x + 2 sin x have a horizontal tangent?

To determine

To find:  the values of x for which fx=x+2sinx have a horizontal tangent.

Explanation

1) Concept:

A horizontal tangent has slope m = 0. The slope of a tangent is calculated by differentiating the function.

2) Formula:

Slope of tangent line is same as derivative of a function.

Slope of horizontal line is zero.

ddxux+vx=ddxux+ddxv(x)

ddxcfx=c ddxf(x)

3) Given:

fx=x+2sinx has a horizontal tangent

4) Calculations:

fx=x+2sinx

ddxfx=ddx x+ddx 2sinx

f'x=1+2cosx

Since slope of horizontal line is zero, equate this derivative with zero

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