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?
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.
