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Mean Value Theorem

★★★☆☆High School

📖Definition

The Mean Value Theorem states for a function continuous on [a,b] and differentiable on (a,b), there exists a point where tangent slope equals secant slope.

📐Formulas

f'(c) = (f(b) - f(a))/(b - a)

Mean Value Theorem (c exists with a < c < b)

✏️Examples

예제 1

Find c for f(x) = x² on [1, 3].

📜History

Discovered by: Augustin-Louis Cauchy (1823)

Cauchy proved it during the rigorization of analysis.

⚡Applications

Analysis

Determining function increase/decrease

Physics

Instantaneous vs average velocity

Error Analysis

Taylor expansion remainder

🔗Related Documents

#평균값#미적분#mean value#calculus