MATH 1271 Midterm: Exam 4 Review
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Suppose that f is continuous on the closed interval [a,b] and let n be any number between f(a) and f(b), where f(a) f(b). Then there exists a number c in (a,b) such that f(c)=n. *plot f to find x sub 0 f[x_]:= To find roots of f(x) to approximate cuberoot(11) If we had a limit at , we could still l"hopital and use dominating terms. If f is a function that satisfies the following hypotheses: Then there is a number c in (a, b) such that f is continuous on the closed interval [a,b] f is differentiable on the open interval (a,b). Yes, f(3)=lim x(cid:574) f(x) so continuous at 3 on [0,3), f is differentiable, hence continuous. Is f differentiable on (0,3)? yes, because the problem gives us that. So, by the mvt, there exits a c in (0,3) s. t. We would be given the mvt on an exam, but we need to know the name of it.
