SOLUTION: 1. Find two positive real numbers whose sum is 40 and whose product is a maximum. (Hint: Construct the function f(x) = x(40-x) ) 2. Explain how y

Question 242928: 1. Find two positive real numbers whose sum is 40 and whose product is a
maximum.
(Hint: Construct the function f(x) = x(40-x) )

2. Explain how you would find the x-intercepts and y-intercept for quadratic
functions? Are there situations where graph of quadratic functions have
only one x-intercept? Situations where there are no x-intercepts?

Answer by JimboP1977(311) (Show Source): You can put this solution on YOUR website!
y= x(40-x)
y=40x-x^2
dy/dx = 40-2x (the gradient of the graph)
We want to know the maximum of the graph ie when it is at its peak and the gradient is 0.
so we set the gradient to equal zero and rearrange to give x = 20.
x-intercepts can be found by factorising the quadratic equation eg the graph of y = x(40-x) crosses the x axis when y = 0. So 0 = x(40-x). Then x must be equal to 0 or 40.
The y intercept is always given when x is 0.
The graph of y=x^2 (green) only has one x intercept. The graph of y=x^2+10 (blue) has none.

RELATED QUESTIONS
Find two positive real numbers whose sum is 40 and whose product is a maxium. Construct... (answered by longjonsilver)

Find two positive real numbers whose sum is 40 and whose product is maximum without... (answered by drk)

1.The amount of copper ore produce from a copper mine in Arizona is modeled by the... (answered by Boreal)

Find two positive real numbers whose product is a maximum. The sum is 978. (answered by Boreal)

Find two numbers whose sum is 56 and whose product is as large as possible. [Hint: Let x... (answered by stanbon,Alan3354)

Find two positive real numbers whose sum is 70 and their product is... (answered by Alan3354)

Find two positive real numbers whose sum is 26 and product is... (answered by ikleyn)

Find two positive real numbers with a maximum product whose sum is... (answered by stanbon)

Find two numbers whose difference is 60 and whose product is as small as possible. [hint: (answered by hkwu)