text: # The weekly cost (C) of growing and selling x acres of flowers is approximated by C = 0.2x^2-12x + 240. How many acres of flowers would minimize these costs?
  
  Apr 8, 2018
  
  $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$
  
  $C ' \left(x\right) = 0.4 x - 12$
  
  Equating this to 0,
  
  $\implies 0.4 x - 12 = 0$
  
  $\implies 0.4 x = 12$
  
  $\implies x = 30$
  
  Again, taking derivative of $C ' \left(x\right) = 0.4 x - 12$
  
  $C ' ' \left(x\right) = 0.4$
  
  $C ' ' \left(x\right) > 0$
  
  Hence, $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$ is minimised at $x = 30$.
  
  30 acres of flowers would minimize these costs :)