Answer:
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:
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 4x + 2
Step 2: Find 1st Derivative
- Basic Power Rule: f'(x) = 2·3x²⁻¹ - 1·4x¹⁻¹
- Simplify: f'(x) = 6x - 4
Step 3: Find tangent slope
- Define: f'(x) = 6x - 4, x = 2
- Substitute: f'(2) = 6(2) - 4
- Multiply: f'(2) = 12 - 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.
