Math Problem Statement

Analyze and sketch a graph of the function over the given interval. Find any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. (Round your intercept values to three decimal places. Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.)

FunctionInterval

f(x) = 2x − 4 sin(x)

0 ≤ x ≤ 2𝜋

intercepts

(xy)

=       (xy)

=       relative minimum

(xy)

=       relative maximum

(xy)

=       point of inflection

(xy)

=       Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.)  

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Graphing Functions
Derivatives
Critical Points
Inflection Points
Intercepts
Asymptotes

Formulas

f(x) = 2x - 4 sin(x)
f'(x) = 2 - 4 cos(x)
f''(x) = 4 sin(x)

Theorems

First Derivative Test
Second Derivative Test

Suitable Grade Level

Undergraduate Calculus