Transcript Mean Value Theorem - Lompoc Unified School District


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
f ( b)  f ( a )
f '( c) 
ba
or
f (b)  f (a)  f '(c)(b  a)

Find all values of c that satisfy the mean value
theorem for f ( x)  x3  x 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.