Math Problem Statement
What is the difference quotient of f if f(x)=x^2 +5x -1?
Solution
The difference quotient of a function is given by:
where is a small increment. Given the function , we need to find and then substitute it into the difference quotient formula.
- Calculate :
Expand and :
- Find the difference :
Simplify by canceling out , , and :
- Form the difference quotient:
Simplify by dividing each term by :
So, the difference quotient for is:
Would you like further details on this process or have any questions?
Here are 5 related questions for further exploration:
- How does the difference quotient relate to the derivative of a function?
- What happens to the difference quotient as approaches 0?
- How would you find the derivative of using limits?
- Can you calculate the difference quotient for a different function, such as ?
- What is the significance of the difference quotient in calculus?
Tip: The difference quotient is the foundation for understanding derivatives, which measure the rate of change of a function.
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Math Problem Analysis
Mathematical Concepts
Functions
Difference Quotient
Algebra
Formulas
Difference quotient formula
Theorems
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Suitable Grade Level
Grades 11-12
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