   Chapter 3.1, Problem 41E

Chapter
Section
Textbook Problem

# Find the critical numbers of the function. f ( θ ) = 2 cos θ + sin 2 θ

To determine

To find:

The critical numbers of the given function.

Explanation

1) Concept:

Differentiate f(θ) with respect to θ, and then find the values of θ where f'θ=0 and f'θ doesn’t exist. That gives the critical numbers.

2) Definition:

A critical number of a function f   is a number c in the domain of f  such that either  f'c=0 or f'c does not exist.

3) Given:

fθ=2cosθ+sin2θ

4) Calculation:

Differentiate f(θ) with respect to θ by using the chain rule of derivative.

f'θ=2cosθ+sin2θ'

f'θ=-2sinθ+2sin

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