Math Problem Statement
Find the value of f(x+h) - f(x) /H, if f(x)=x2+7 $$$$
Solution
To find the value of for the function , we need to carefully evaluate each step. Here's the detailed process:
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Evaluate :
Given , substitute into the function:
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Expand :
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Find :
Now, compute the difference: Simplify the expression:
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Divide by :
Simplify the fraction:
So, the value of is .
If you need further clarification or have any questions, feel free to ask!
Here are some related questions to explore:
- What is the derivative of using the limit definition of a derivative?
- How does the expression help in understanding the concept of a secant line?
- What happens to as approaches 0?
- Can you generalize the process of finding for any polynomial function?
- How would you interpret the result in the context of the rate of change?
- What are the implications of this result for the function's behavior near ?
- Can you find for the function ?
- How does the concept of a limit apply to finding derivatives?
Tip: Always double-check your algebraic manipulations, especially when expanding expressions and simplifying fractions. This attention to detail ensures accuracy in your calculations.
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Math Problem Analysis
Mathematical Concepts
Functions
Quadratic Equations
Limits
Formulas
Quadratic function formula: f(x) = x^2 + 7
Limit definition of a derivative
Theorems
Definition of a derivative
Suitable Grade Level
Grades 11-12