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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