 On any continuous function between points a and b there exists some point(s) c where the tangent line at this point has the same slope as the secant.

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Presentation transcript:

 On any continuous function between points a and b there exists some point(s) c where the tangent line at this point has the same slope as the secant line between a and b

Let f be a function that satisfies 1) f is continuous on [ a, b ] 2) f is differentiable on [ a, b] Then there is a number c in [ a, b] such that or

 Find all values of c that satisfy the mean value theorem for on [ 0, 2]

 Two stationary patrol cars equipped with radar are 5 miles apart on a highway. A truck passes the first car and is clocked at 55 mi/hr. Four minutes later it passes the second car and is clocked at 50 mi/hr. Prove that the truck must have exceeded the speed limit (55) at some time during these 4 minutes.