## Math Problem Statement

- Given f(x) = 2x 2 − x + 2, use the limit definition m = lim h→0 f(a + h) − f(a) h or limx→a f(x) − f(a) x − a to find the slope of the tangent line to the curve at x = 2. Use your result to write an equation of the tangent line at x = 2

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Calculus

Derivatives

Limits

Tangent Line

### Formulas

Limit definition of the derivative: m = lim h→0 [f(a+h) − f(a)] / h

Point-slope form of a line: y − y₁ = m(x − x₁)

### Theorems

Derivative as the slope of the tangent line

### Suitable Grade Level

Grades 11-12

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