Math Problem Statement
f(x) = x^2 + 8x; f'(4) = ?
Solution
The given problem is:
We are asked to find the derivative of at , i.e., .
Step 1: Find the derivative .
To find the derivative, we'll differentiate with respect to .
Step 2: Calculate .
Now, substitute into .
So, the value of is 16.
Would you like more details or have any questions?
Here are some related questions:
- What is the general formula for the derivative of a polynomial function?
- How do you find the derivative of a function using the power rule?
- What is the significance of the derivative in real-world applications?
- How do higher-order derivatives relate to the original function?
- What does the derivative tell us about the behavior of the function at a given point?
Tip: Always double-check your differentiation steps to ensure the accuracy of your derivative calculations.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Polynomial Functions
Formulas
Derivative of f(x) = x^2 + 8x: f'(x) = 2x + 8
Theorems
Power Rule of Differentiation
Suitable Grade Level
Grades 9-12