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Theorems

QuestionAnswer
Mean Value Theorem (MVT) f'(c) = f(b) - f(a) / b - a
What does the MVT say? There is a value c in the interval (a,b) such that the instantaneous slope equals the average slope
What does the IVT say? For any number N between f(a) and f(b), there exists at least one number c in (a,b) such that f(c) = N
What does the EVT say? A function f attains both an absolute minimum and an absolute maximum on the interval [a,b]
What is the MVT used for? To find where the slope of a tangent line equals the slope of the secant line
What is the IVT used for? To prove that a function hits a specific value within an interval
What is the EVT used for? Guarantees absolute extrema exist, found by checking critical points and endpoints
Created by: user-1882782
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