posted by Jen .
The geometric mean of two postitive numbers a and b is sqrt(ab).
Show that for f(x) = 1/x on any interval [a,b] of positive numbers, the value of c in the conclusion of the mean value theorem is c = sqrt(ab)
I have no idea how to do this!
If the mean of a and b is sqrt(ab), then (a + b) / 2 = sqrt(ab).
Is c supposed to be the area under the graph in interval [a,b] ? If so, calculate the antiderivative of f(x) and you'll have the formula for c.
It is the geometric mean. Isn't (a+b)/2 the arithmetic mean?