The volume (in m3) of water in my (large) bathtub when i pull out the plug is given by f(t)=4−t2 (t is in minutes). this formula is only valid for the two minutes it takes my bath to drain.
(a) find the average rate the water leaves my tub between t=1 and t=2
(b) find the average rate the water leaves my tub between t=1 and t=1.1
(c) what would you guess is the exact rate water leaves my tub at t=1
(d) in this bit h is a very small number. find the average rate the water leaves my tub between t=1 and t=1+h (simplify as much as possible)
(e)
what do you get if you put in h=0 in the answer to (d)?