Mean Value Theorem - Lompoc Unified School District
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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)
ba
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.