Math Problem Statement
Solution
Let's go through the problem step by step.
We are given the function: We need to find:
- The difference quotient:
1. Finding :
Substitute into the function :
2. Finding :
Substitute into the function:
3. Finding the difference quotient:
Substitute the expressions for and : Simplify the numerator: Cancel out (since ):
Final answers:
Would you like further details or clarifications on any part of this solution?
Here are 5 related questions for practice:
- What is the derivative of the function ?
- Find the difference quotient for the function .
- What is the physical interpretation of the difference quotient in real-world problems?
- How does the difference quotient relate to the slope of a secant line?
- How would the difference quotient change if we used a quadratic function?
Tip: The difference quotient is the foundation of the derivative. Understanding how it works will help you with concepts in calculus, especially when studying limits and instantaneous rates of change.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Difference Quotient
Formulas
f(x) = 8 - 7x
Difference Quotient = [f(a + h) - f(a)] / h
Theorems
Linear Function Analysis
Suitable Grade Level
Grade 10-12 (Pre-Calculus)
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