Question

Help me answer this question please​

Answer 1

f'(2) = 8

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

Calculus

The definition of a derivative is "the slope of the tangent line".

Derivatives of constants are 0.

Basic Power Rule:

• f(x) = cxⁿ

• f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

f(x) = 3x² - 4x + 2

Step 2: Find 1st Derivative

1. Basic Power Rule: f'(x) = 2·3x²⁻¹ - 1·4x¹⁻¹
2. Simplify: f'(x) = 6x - 4

Step 3: Find tangent slope

1. Define: f'(x) = 6x - 4, x = 2
2. Substitute: f'(2) = 6(2) - 4
3. Multiply: f'(2) = 12 - 4
4. Subtract: f'(2) = 8

Step 4: Identify

f'(2) = 8 tells us that at x = 2, the slope of the tangent line is 8.