Math Problem Statement
the Difference Quotient for f(x) = -x^2-x+5
Solution
To find the Difference Quotient for the function , we use the following formula:
Step 1: Find
Substitute into :
Expanding this expression:
Step 2: Difference Quotient
Now, substitute and into the Difference Quotient formula: Simplify the numerator: This simplifies to:
Step 3: Simplify the Difference Quotient
Now, divide the simplified expression by :
Thus, the Difference Quotient for is:
Would you like any further details on this process or any clarifications?
Here are 5 related questions you might find helpful:
- How is the Difference Quotient used to find the derivative of a function?
- What is the Difference Quotient for a linear function?
- Can the Difference Quotient be applied to trigonometric functions?
- How does the Difference Quotient change for functions with higher powers of ?
- How can we interpret the result of the Difference Quotient geometrically?
Tip: The Difference Quotient formula is the foundation of the derivative, which gives the slope of the tangent line at any point on a curve.
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Math Problem Analysis
Mathematical Concepts
Algebra
Calculus
Difference Quotient
Formulas
Difference Quotient: (f(x+h) - f(x)) / h
Theorems
Concept of the Difference Quotient as a foundation for the derivative
Suitable Grade Level
Grades 11-12 (Pre-Calculus/Calculus)