AP Calculus ABmediummcq1 pt
The Mean Value Theorem states that if f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that:
A.f(c) = [f(b) - f(a)]/2
B.f'(c) = [f(b) - f(a)]/(b - a)
C.f(a) = f(b)
D.f'(c) = 0
Explanation
Core Concept
The MVT guarantees a point c where the instantaneous rate of change equals the average rate of change over [a,b]: f'(c) = [f(b) - f(a)]/(b - a).
Correct Answer
Bf'(c) = [f(b) - f(a)]/(b - a)
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