Find Two Positive Real Numbers Whose Product Is a Maximum
So x 54 - 3y. Differentiate to find the critical points. If Am And Gm Of Two Positive Numbers A And B Are 10 And 8 Respectively Find The Numbers The maximum product occurs when all the terms are equal ie. . F is maximum when dfdy 0. The two positive real numbers are 9 33. Suppose the numbers are x and 2y with x 2y 32. Y 40 x. We would like to find where the product x y is maximum but from the above equation we can write. Okay so this I can work with. Let the first and second number be x and y. Part 1 1 Step 1 Let x be the first number and y be the second number. I cant really work with this now. Then the first number is 16-2x. F x 100 2 x 100 2 x 0 2 2 0 Since it is positive it means that yes there is a minimum. Find two positive numbers whose product is 100 and their sum is a minimum. Plugging into the first equation we get 24 3y 48. Use the second derivative test to dete...