MATH 140 Lecture Notes - Lecture 14: Mean Value Theorem
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3. (a) f f f f(b) is continuous on the closed interval a, b] is differentiable on the open interval a, b) Then there is a number c in a, b) such that (c) f . 2. f f is continuous on the closed interval a, b] is differentiable on the open interval a, b) Then there is a number in a, b) such that c f(b) f(a) b a f(a) f . Or 2. (b) f f (c)(b a) in an interval for all. , then x f a, b) in an interval f g (x) (x) x is a constant (x) c. Corollary: if (x) that is, f is constant on a, b) is constant on f g a, b) Prove that the equation x3 + = = 3 + 1 x. Since is a polynomial, it is continuous, so the ivt states that there is f number c such that between.
