For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function F defined by F(t)=arctan(π2−t10) . For time 5≤t≤10 , water is leaking from the tub at a rate given by the function L defined by L(t)=0.03(20t−t2−75) . Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by W(t) . (a) At time t=3 , there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3 , and use it to approximate the volume of water in the tub at time t=3.5 .