MTH 114 Study Guide - Final Guide: Mean Value Theorem
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If f"(c)=0 or does not exist, and c is in the domain of f, then c is a what? (derivative is 0 or undefined) If we let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f"(c)=0 (if the slope of the secant is. 0, the derivative must = 0 somewhere in the interval). What theorem states that the instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line. The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line. f "(c) = [f(b) - f(a)]/[b - a] Let c be a critical number of a function f that is continuous on the closed interval.
