Question 1188657: 1. Find two positive real numbers whose sum is 40 and whose product is maximum.
2. An arrow is shot upward with an initial velocity of 80 feet per second. The height of the arrow, h(t), in terms of the time since the arrow was released t, is h(t)= 80t - 16t². How long after the arrow is released does it reach its maximum height? What is the maximum height?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Let one number be 20+x. Then the other number is 20-x,
and their product is (20+x)*(20-x) = 400 - 4x^2.
Looking at this quadratic form, it is obvious that the maximum is at x = 0;
so the numbers are 20 and 20.
ANSWER. The product of such numbers is maximum when the numbers are equal, x= 20 and y= 20.
Solved.
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