Problem
of
the
Week

PROBLEM 24

This week's problem was suggested by Dr. Michael McAsey of Bradley University.

The Mean Value Theorem for Integrals states that if f is a continuous function on the inteval [a,b], then there exists a number c between a and b so that

MEAN VALUE INTEGRAL.

This means (for non-negative functions) that the area under the graph of f is the same as the rectangle of base length b-a and height f(c).

Consider now the function c(t) defined by allowing the upper limit on the integral to vary,

MEAN VALUE FUNCTION.

Find the derivative dc/dt.

You may wish to make some assumptions about the function f. Just let me know what they are.

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