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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.)