Math Problem Statement
For y=x-6/x+5, find the average rate of change from -4 ≤x ≤-1.
Solution
To find the average rate of change of over the interval , we use the formula:
where , , and are the values of at and , respectively.
Step 1: Compute at
Step 2: Compute at
Step 3: Calculate the average rate of change
Substitute , , , and into the formula:
Simplify the numerator and denominator:
Simplify the fraction:
Final Answer:
The average rate of change is:
Would you like a deeper breakdown or further assistance?
Related Questions:
- How do you interpret the average rate of change in this context?
- What happens if , where the denominator becomes zero?
- How would the interval change the result if it were ?
- Can you derive a general formula for the average rate of change of this function over any interval?
- What is the significance of the slope being positive, negative, or zero in this scenario?
Tip:
Always check for points where the denominator might become zero when working with rational functions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Average Rate of Change
Formulas
Average Rate of Change = (y2 - y1) / (x2 - x1)
Theorems
Properties of Rational Functions
Suitable Grade Level
Grades 10-12
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