Question

The yield in bushels from a grove of orange trees is given by Y = x(200 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?

Answer 1

Y=x(200-x)

or, Y=200x-x²

here we use differential of Y for maximization/minimization problem

after getting differential we get

, dY/dx=200-2x

putting dY/dx=0 and it imply 200-2x=0

or . 2x=200

or, x=100

the second derivative of Y is d²y/dx2=-2, so Y is maximum for x=100

so answer is 100, i.e.   100 trees will maximize the yield.