Math Problem Statement

Find the difference quotient \(\frac{f(x+h) - f(x)}{h}\) and fully simplify your answer.

Solution

The problem in the image asks you to find the difference quotient f(x+h)f(x)h\frac{f(x+h) - f(x)}{h} and fully simplify your answer.

To solve this problem, we'll follow these general steps:

  1. Substitute x+hx + h into the function: Compute f(x+h)f(x + h).
  2. Subtract the original function: Find the expression for f(x+h)f(x)f(x + h) - f(x).
  3. Divide by hh: Simplify the expression f(x+h)f(x)h\frac{f(x + h) - f(x)}{h}.

To proceed with a specific solution, the function f(x)f(x) needs to be given. Since it's not included in the cropped image, can you provide the function f(x)f(x) so that I can fully solve this problem?


If you'd like, I can help with the solution by providing example functions such as f(x)=x2f(x) = x^2 or any other function you have in mind.

Let me know if you'd like to proceed or if you have any specific function to work with.

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Math Problem Analysis

Mathematical Concepts

Calculus
Difference Quotient
Functions

Formulas

Difference Quotient: \(\frac{f(x+h) - f(x)}{h}\)

Theorems

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Suitable Grade Level

Grades 11-12