Find Two Positive Real Numbers Whose Product Is a Maximum

Find two positive real numbers whose product is a maximum. How do you find the two positive real numbers whose sum is 40 and whose product is a maximum.

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Let P xy y30-3y 0n differentiating P with respect to y we get.

. Tutorial Exercise Find two positive real numbers whose product is a maximum. The two positive real numbers are 9 33. Enter your answers as a.

On putting we get. The sum of the first and three times the second is 36. The product of one by the square of the other is to be a maximum.

Solve for the value of y y y. S2-x S2-x S22- x2. Xymaximum which is unknown.

Y 40 x. Let a be the first number and b. Let the sum be S first number S2- x second number S- S2-x S2x.

X y x 40 x x2 40x. Let first number be 𝑥 Now given that First number Second number 24 𝑥 second number 24 Second number 24 𝑥 Product 𝑓𝑖𝑟𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑥 24𝑥 Let P𝑥 𝑥 24𝑥 We need product as large as possible Hence we need to find maximum value of P𝑥 Finding Px P𝑥𝑥24𝑥 P𝑥24𝑥𝑥2 P𝑥242𝑥 P𝑥212𝑥 Putting P. Find two numbers whose sum is 9 if the product of one by the square of the other is a maximum.

Find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum. Step 1 Let x be the first number and y be the second number. F is maximum when dfdy 0.

Their product is fxy xy and since the sum of the first and three times the second is 54 we have x 3y 54. Second number is y. X y 110 begin aligned x y 110 end aligned x y 110.

F x 100 2 x 0 100 2 x 100 2 x x 100 2 50 Now find the second derivative of the function f x. Then the first number is 16-2x. We would like to find where the product x y is maximum but from the above equation we can write.

We want to find the numbers to get the maximum value of the product x 16-2x. Since x is real its square is always positive and therefore the product is maximum and equal to S2. As sum of the first number and three times the second number is 30 x 3y 30.

Enter your answers as a comma-separated list The sum of the first and twice the second is 16. Let the first and second number be x and y. The sum of the two numbers is k.

Find two positive numbers whose product is 100 and their sum is a minimum. Let x x and y y be two positive numbers such that x 2y 50 x 2 y 50 and x 1y 2 x 1 y 2 is a maximum. To do that we calculate the derivative f x 2x 40 and we look for values of x.

Three times the second number 3y. If we look at the field from above the cost of the vertical sides are 10ft the cost of the bottom is 2ft and the cost of the top is 7ft. Use the second derivative test to determine whether the number we found was a critical number.

1 the sum is s. Enter your answers as a comma-separated list The sum of the first and twice the second is 16. The way you put your question is meaningless.

Substitute x 50 into y x 100. X y x 40 x x2 40x. Find two positive numbers whose product is a maximum.

Write an equation to show that the sum of the two positive real numbers is 110. Learn how to maximize the product of 2 numbers given a constraint in this free math video tutorial by Marios Math Tutoring. Y 36 36 Step 2 Solve your equation in the previous step for y 36-X 3 y 36 - 3 Step 3 The product P of the.

F x 100 2 x 100 2 x 0 2 2 0 Since it is positive it means that yes there is a minimum. Write an equation describing the sum in this problem. This is as far as Ive gotten in solving it.

What are two positive real numbers whose product is a maximum. Let x and y be the two positive real numbers. The sum of the first and three times the second is 36.

So we now have a one-variable function f x x2 40x and must find a positive value of x where the function f reaches a maximum. Solve for x which comes out to be x-4y120. Two real numbers whose sum is S and whose product is a maximum.

Fy 54y - 3y². So dfdy d54y - 3y²dy. Enter your answers as a comma-separated list the sum of the first and three times the second is 54.

First number is x. Let x x x and y y y be the two positive real numbers. Find two positive real numbers whose product is a maximum.

We would like to find where the product x y is maximum but from the above equation we can write. Substituting x into f we have. Find two positive real numbers such that the sum of the first number squared and the second number is 243 and their product is a maximum.

We get x 30 - 3y. So x 54 - 3y. Find two positive real numbers whose product is a maximum.

1 the sum is s. Let the second number be x. This problem involves working wi.

Find two positive numbers whose product is a maximum. Fy 54 - 3yy. How to find the two positive real numbers.

We need to find two positive real numbers whose product is maximum. Math Trigenometry Find two positve real numbers whose product is a maximum and whose sum of the first number and four times the second number is 120. We are going to fence in a rectangular field.

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