Math Problem Statement
its x^2 not x^3
Solution
Thank you for the clarification. Let's go through the steps again with the correct function .
Step 1: Find the derivative of .
The function is: The derivative with respect to is:
Let's differentiate each term:
- (since the derivative of a constant is zero)
So, the derivative is:
Step 2: Evaluate the derivative at .
Substitute into :
Final Answer:
The rate of change of the function at is .
Would you like more details or have any questions?
Here are five related questions you might find useful:
- How does changing the coefficients in a quadratic function affect its derivative?
- What is the geometric interpretation of the rate of change for a quadratic function?
- How do you determine the maximum or minimum points using the derivative?
- How can you apply the concept of derivatives to real-world problems, such as velocity?
- What is the significance of the sign of the derivative in different intervals of the function?
Tip: Always ensure that the correct form of the function is used before performing calculations to avoid errors in the final result.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Quadratic Functions
Formulas
Derivative rules
Theorems
-
Suitable Grade Level
Grades 11-12
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