Question

What is the minimum value of $f(x)=3 \cos 2 x ?[4.3]$

   What is the minimum value of $f(x)=3 \cos 2 x ?[4.3]$

Essentials of Precalculus

Essentials of Precalculus

Richard N. Aufmann,… 1st Edition

Chapter 4, Problem 75

Instant Answer

Solved by Expert Monica Miller

07/22/2021

Step 1

That is, $-1 \leq \cos(2x) \leq 1$. Show more…

Show all steps

lock

Thanks for your feedback!

What is the minimum value of $f(x)=3 \cos 2 x ?[4.3]$

Play audio

Feedback

Powered by NumerAI

Monica Miller and 59 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cosine Function Properties

The cosine function is inherently periodic and oscillates between -1 and 1. This characteristic is crucial when determining the behavior of any function derived from it, as it defines the upper and lower limits of the function's output.

Amplitude Adjustment

Multiplying a trigonometric function by a constant scales its output. In the case of the cosine function, this means that the maximum and minimum values are multiplied by the constant, directly impacting the range of the function.

Range of Transformed Trigonometric Functions

Understanding how basic transformations affect the cosine function is fundamental. When the function is scaled, its range is adjusted proportionally, which allows one to determine the new extrema by applying the constant to the original boundaries of -1 and 1.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later