3.4 Derivatives of Trigonometric Functions

Mathematica script by Chris Parrish,
cparrish@sewanee.edu

Problems from James Stewart,
"Calculus: Concepts and Contexts,"
Second Edition, Brooks/Cole, 2001

Gallery of Some Trigonometric Functions and Their Derivatives

Stewart, Section 3.4

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Finding Horizontal Tangents

Stewart, Section 3.4, Example 2

First, let's define and then differentiate a certain trigonometric function f.

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Now, try to discover where the graph of f has a horizontal tangent.
Ans: The graph of f has a horizontal tangent when f'(x) == 0.

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We were warned by Mathematica to check the points 3π/4 and -π/4 by hand.
Should we retain or discard those points?
Should we retain or discard the points which Solve returned: -3π/4 and π/4 ?

Taking into account the periodicity of the trigonometric functions involved,
what is the complete list of ALL of the points where f'(x) == 0 ?

Created by Mathematica  (April 19, 2004)