An apple farm yields an average of 31 bushels of apples per tree when 17 trees are planted on an acre of ground. each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. how many trees should be planted on an acre in order to get the highest yield?

There are 31 bushels of apples when the number of trees is 17 but decreases by 1 for each additional tree x:           
              Yield = (17 + x) * (31 - x)                                                                               
                       = 527 - 17x + 31x - x2                     
                       = 527 + 14x - x2
We know that for function f(x), the derivative df(x)/dx is zero at maximum point x. We can take the derivative of the yield then set it to zero to find x:           
              d(Yield)/dx = 14 - 2x                         
                             0 = 14 - 2x                       
                           2x = 14                          
                             x = 7
Therefore there should be 17 + 7 = 24 trees to be planted on an acre in order to get the highest yield.