Math Problem Statement

f(x) = x^2 + 8x; f'(4) = ?

Solution

The given problem is:

f(x)=x2+8xf(x) = x^2 + 8x We are asked to find the derivative of f(x)f(x) at x=4x = 4, i.e., f(4)f'(4).

Step 1: Find the derivative f(x)f'(x).

To find the derivative, we'll differentiate f(x)f(x) with respect to xx.

f(x)=ddx(x2+8x)=2x+8f'(x) = \frac{d}{dx}(x^2 + 8x) = 2x + 8

Step 2: Calculate f(4)f'(4).

Now, substitute x=4x = 4 into f(x)f'(x).

f(4)=2(4)+8=8+8=16f'(4) = 2(4) + 8 = 8 + 8 = 16

So, the value of f(4)f'(4) is 16.

Would you like more details or have any questions?

Here are some related questions:

  1. What is the general formula for the derivative of a polynomial function?
  2. How do you find the derivative of a function using the power rule?
  3. What is the significance of the derivative in real-world applications?
  4. How do higher-order derivatives relate to the original function?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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