MATH 1131Q Lecture Notes - Lecture 9: Mean Value Theorem, Maxima And Minima, Inflection
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Math 1131q , lecture 9 , sections 4. 2 / 4. 3 / 4. 4. Let f be a function that satisfies the following three hypotheses: 3. f is continuous on the closed interval [a,b] f is differentiable on the open interval (a,b) f(a) = f(b) Then there is a number x in (a,b) such that f"(c) = 0. Let f be a function that satisfies the following hypotheses: f is continuous on the closed interval [a,b] f is differentiable on the open interval (a,b) Then there is a number c in (a,b) such that f"(c) = f(b) - f(a) A or f(b) - f(a) = f"(c) (b-a) In order to apply rolle"s theorem to h(x) , we need to check the three hypotheses: h is continuous on the closed interval [a,b, h is differentiable on the open interval (a,b, h(a) = h(b) How derivatives affect the shape of a graph.
