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 determine whether the number we found was a critical number. X y 110 begin aligned x y 110 end aligned x y 110.

Let x and y be the two positive real numbers. The sum of the first and three times the second is 48. Fy 54 - 3yy.

How do you find the two positive real numbers whose sum is 40 and whose product is a maximum. Enter your answers as a comma-separated list The sum of the first and twice the second is 16. We want to find the numbers to get the maximum value of the product x 16-2x.

Let the second number be x. Fy 54y - 3y². Find two positive real numbers whose product is a maximum.

Let P xy y30-3y 0n differentiating P with respect to y we get. As sum of the first number and three times the second number is 30 x 3y 30. Their product is fxy xy and since the sum of the first and three times the second is 54 we have x 3y 54.

Find two positive numbers whose sum is 100 and whose product is a maximum. How to find the two positive real numbers. This is as far as Ive gotten in solving it.

Well just call him X. Second number is y. X y x 40 x x2 40x.

And in this problem the some must be X which means that we have to two numbers to real positive numbers will take them to be X. Write an equation to show that the sum of the two positive real numbers is 110. Call the two numbers x and y.

A x 100-x 100x - x 2. We would like to find where the product x y is maximum but from the above equation we can write. Solve for x which comes out to be x-4y120.

Substituting x into f we have. 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. Setting this equal to 0 we get 2x 48.

We wish to maximize the product xy. First number is x. Find two positive real numbers whose product is a maximum.

The sum of the first and three times the second is 36. 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. Heres a problem that asked us to find two positive real numbers whose product is a maximum right.

On putting we get. Three times the second number 3y. Replace x2y with 32 to obtain hence the maximum product is 128.

Whatever that maximum is. Enter your answers as a comma-separated list The sum of the first and three times the second is 42. To do that we calculate the derivative f x 2x 40 and we look for values of x.

Using the AM-GM inequality. Enter your answers as a comma-separated list the sum of the first and three times the second is 54. The constraint is that x y 100 and we need to maximise Axy.

So dfdy d54y - 3y²dy. Write an equation describing the sum in this problem. Okay So for this problem were going to find two positive real numbers whose maximum is whose products.

We need to find two positive real numbers whose product is maximum. Let x x x and y y y be the two positive real numbers. Distributing we get 48x-x23.

We get x 30 - 3y. And then the some of the first number and twice the second number is equal to 24. X y x 40 x x2 40x.

Rearrange the constraint to y 100 - x and substitute into the product equation. Find two positive real numbers whose product is a maximum. Find two positive real numbers whose product is a maximum.

X 2y which implies x 16 and 2y 16 y 8. What are two positive real numbers whose product is a maximum. 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.

Multiplying the two numbers we get. Next we need to take the derivative which is 482x3. 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.

Xymaximum which is unknown. Substitute x 50 into y x 100. Find two positive real numbers whose product is a maximum.

Solve for the value of y y y. So our numbers are 16 and 8. Let a be the first number and b.

Enter your answers as a comma-separated list The sum of the first and twice the second is 16.

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