Math Problem Statement
Given f(x) = 1/x+11, find the average rate of change of f (x) on the interval [3,3 + h] your answer will be a expression involving h
Solution
To find the average rate of change of the function on the interval , we use the formula for the average rate of change:
Step 1: Find
Substitute into the function:
Step 2: Find
Substitute into the function:
Step 3: Calculate the difference in function values
Now subtract from :
The 11's cancel out, so you're left with:
Step 4: Simplify the difference
To simplify , we combine the fractions:
Step 5: Divide by
Now, divide the result by to find the average rate of change:
Final Answer:
The average rate of change of on the interval is:
Would you like further details or clarifications?
Related Questions:
- How do you find the instantaneous rate of change of at ?
- What is the derivative of ?
- Can you generalize the average rate of change for any interval ?
- What happens to the average rate of change as ?
- How would the result change if the function was ?
Tip: The average rate of change is closely related to the concept of the derivative, which gives the instantaneous rate of change at a specific point.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Average Rate of Change
Formulas
Average Rate of Change = (f(b) - f(a)) / (b - a)
f(x) = 1/x + 11
Theorems
Difference Quotient (used in rate of change)
Suitable Grade Level
Grades 10-12
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