Answered: Sketch a graph over the given interval,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 56E

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Question

Sketch a graph over the given interval, with all transition points indicated.

y = x + sinx [0, 2pi]

Expert Solution

Step 1

Given data:

The expression for the given function is y=x+sinx.

The given limit of x is [0, 2π].

Transition points are those points where the function changes its sign.

$\begin{array}{rcl} \frac{d^{2} y}{d x^{2}} & = & 0 \\ \frac{d}{d x} (\frac{d}{d x} (x + \sin x)) & = & 0 \\ \frac{d}{d x} (1 + \cos x) & = & 0 \\ 0 - \sin x & = & 0 \\ x & = & 0, π, 2 π \end{array}$

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