Consider the function
f(x)=ax(25-x)
on the interval
0,25
, where
a
is a positive real number. a. Find the average value of
f
as a function of a. b. Find the points at which the value of
f
equals its average value, and prove that they are independent of a. a. The average value of
f
as a function of
a
is
/bar (f)=
◻
(Type an exact answer.)