Question
upstudy study bank question image url

Question
Given the function , determine the average rate of
change of the function over the interval .
Answer
Show Examples

Ask by Summers Frazier. in the United States
Jan 29,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The average rate of change of the function over the interval is 1.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To find the average rate of change of the function over the interval , you need to calculate and , and then use the formula for average rate of change, which is given by:
First, calculate :
Next, calculate :
Now, substitute the values into the average rate of change formula:
So, the average rate of change of the function over the interval is .
For a bit of historical flavor, calculus was developed in the 17th century with foundational contributions from Isaac Newton and Gottfried Wilhelm Leibniz. They formulated the concept of limits and rates of change during the rise of physics and engineering - a time when understanding movement and change was revolutionary!
Now, if you ever get confused by functions and rates of change, remember to plot them! A quick sketch can visually show you where the function rises and falls. Many folks make the mistake of forgetting how crucial it is to understand the graph, which can save you from pesky calculation errors and give you intuitive insight into what’s happening between those points!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy