Algebraic rooting #3
Calculus
Level
3
There are 50 apple trees. Each tree produces 800 apples and if an additional tree is planted , output drops by 10 apples. How many more trees must be planted for maximum output?
The answer is 15.
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1 solution
when we add X trees , the operating equation of this problem is : ( 5 0 + X ) ( 8 0 0 − 1 0 X )
that is : − 1 0 X 2 + 3 0 0 X + 4 0 0 0 0
differentiating the equation to have local critical points , then :
− 2 0 X + 3 0 0
equating this to zero to get the max point , then
X = 1 5 #