The function P(x)=1.25x2+500x4500\displaystyle {P}{\left({x}\right)}=-{1.25}{x}^{{2}}+{500}{x}-{4500} gives the profit when x\displaystyle {x} units of a certain product are sold. Find
a) the profit when 70 units are sold
  dollars
b) the average profit per unit when 70 units are sold
  dollars per unit
c) the rate that profit is changing when exactly 70 units are sold
  dollars per unit
d) the rate that profit changes on average when the number of units sold rises from 70 to 140.
  dollars per unit
e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.)
  units