https://file.aiquickdraw.com/mathbot/file/1726471988651y6mrvtqh.jpg

The problem asks to find and simplify the expression \(\frac{f(a+h) - f(a)}{h}\), given that \(f(x) = 2x^2 - 1\).

Let's break down the steps:

1. **Step 1**: Find \(f(a+h)\).
   - Substitute \(a + h\) into \(f(x)\):
     \[
     f(a+h) = 2(a+h)^2 - 1
     \]
     Expand \((a+h)^2\):
     \[
     f(a+h) = 2(a^2 + 2ah + h^2) - 1 = 2a^2 + 4ah + 2h^2 - 1
     \]

2. **Step 2**: Find \(f(a)\).
   - Substitute \(a\) into \(f(x)\):
     \[
     f(a) = 2a^2 - 1
     \]

3. **Step 3**: Substitute both expressions into \(\frac{f(a+h) - f(a)}{h}\):
   \[
   \frac{f(a+h) - f(a)}{h} = \frac{(2a^

Untuk f(x) = 2x^2 - 1, cari dan sederhanakan [f(a + h) - f(a)] / h.

This problem involves simplifying the difference quotient for the function f(x) = 2x^2 - 1. Follow the steps to find f(a + h) and f(a), and apply the formula [f(a+h) - f(a)] / h. Suitable for students in Grades 10-12 studying algebra and limits.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation