# Applying the Derivative

1. Find two numbers x and y whose sum is 120 and whose product is a maximum.

2. none

3. x + y = 120
xy = maximum
x = 120 - y
I wrote these down but I don't know what to do next. Can you please show me? :) Thank You!!

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danago
Gold Member
Well you have the function P = xy which you want to maximize, however it contains two variables. Are they independent though? How can you reduce this function down to a single variable function?

HallsofIvy
Homework Helper
1. Find two numbers x and y whose sum is 120 and whose product is a maximum.

2. none

3. x + y = 120
xy = maximum
x = 120 - y
I wrote these down but I don't know what to do next. Can you please show me? :) Thank You!!
Replace the x in xy with 120- y so you have only one variable. Now, do you know how to "apply the derivative" to find where a function has a maximum or minimum?

Mark44
Mentor
As an alternate approach, the graph of your area function, as a function of either x or y alone, is a parabola. You can find the vertex of the parabola, at which the maximum area is attained, without using calculus.

HallsofIvy