Math Problem Statement

Let[a,b]R be such that f' * (x) = 0 cach point in (a,b). Prove that f is constant in [a,b]

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Continuity

Formulas

f'(x) = 0 for all x in (a, b)
Mean Value Theorem formula: f'(ξ) = (f(d) - f(c)) / (d - c)

Theorems

Mean Value Theorem

Suitable Grade Level

Grades 11-12