(c). Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in seconds) is given by the function P() =3~ + 3e' +10, /20. (i) What is the size of the population after 1 minute? (1i) Find the average rate of change of P at t = 2 and t = 6? (mi) How fast is the size of the population changing after 1 minute?(d). Use an appropriate technique to find the derivative of the following functions: V4+3x2 V= (x' + 1 )135. (11) 1 + sec y