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Solved: Find Two Positive Numbers That Satisfy The Given Requirements: The Sum Is S And The Product Is A Maximum (Smaller Value) (Larger Value) Need Help? Read It Watch It

The sum is $S$ and the product is a maximum. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams. So positive numbers. But we also know that. So what we can do here is first get X as a function of Y and S. Or alternatively Y is a function of X. Let this be a equation number two. NCERT solutions for CBSE and other state boards is a key requirement for students. The sum is s and the product is a maximum unit. Now compute the first derivative P dash of X is equals to As -2 x. Finding Numbers In find two positive numbers that satisfy the given requirements. Doubtnut helps with homework, doubts and solutions to all the questions.

The Sum Is S And The Product Is A Maximum Unit

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The Sum Is S And The Product Is A Maximum Integer

I couldn't find a discussion of this online, so I went and found the solution to this, and then to the general case for a sum of S instead of 10. Now we have to maximize the product. Doubtnut is the perfect NEET and IIT JEE preparation App. Such time productive maximized. What is the maximum possible product for a set of numbers, given that they add to 10? You have to find first a function to represent the problem stated, and then find a maximum of that function. Try Numerade free for 7 days. Answered step-by-step. We want to find when the derivative would be zero. Get 5 free video unlocks on our app with code GOMOBILE. How do you find the two positive real numbers whose sum is 40 and whose product is a maximum? | Socratic. Math Image Search only works best with zoomed in and well cropped math screenshots. Now the second derivative. I hope you find this answer useful. Now we want to maximize F of X.

The Sum Is S And The Product Is A Maximum Difference

1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc. Finding Numbers In Exercises $3-8, $ find two positive numbers that satisfy the given sum is $S$ and the product is a maximum. It has helped students get under AIR 100 in NEET & IIT JEE. This implies that X is equals to S by two. So the way we do that is take the derivative with respect to X. The numbers are same. We would like to find where the product. The numbers must be real and positive, but [and this was not allowed in the other versions I saw] they do not need to be integers or even rational. How do you find the two positive real numbers whose sum is 40 and whose product is a maximum? The sum of two number is constant. Show that their product will be maximum if each number is half of their sum. That means we want to X two equal S Or X two equal s over to having that we have that Y equals s minus S over two, or Y equals one half of S. So we have in conclusion that the two numbers, we want to X and Y would equal S over to and S over to. And we want that to equal zero. Now we compute B double derivative pw dash off X is equals to minus two which is less than zero. For this problem, we are asked to find numbers X and Y such that X plus Y equals S. In the function F of x, Y equals X times Y is maximized. If someone has seen it solved/explained before, they might be able to point me towards a discussion with more depth than I've gotten to so far.

So to conclude the value obtained about we have b positive numbers mm hmm X-plus y by two and X plus by by two. And s fact, I'll do that. Now substitute the value of life from equation to such that P of X is equals to X times as minus X is equals to S X minus x. There is no restriction on how many or how few numbers must be used, just that they must have a collective sum of 10. SOLVED: Find two positive numbers that satisfy the given requirements: The sum is S and the product is a maximum (smaller value) (larger value) Need Help? Read It Watch It. Solved by verified expert. Find two positive real numbers whose product is a sum is $S$. Join MathsGee Student Support, where you get instant support from our AI, GaussTheBot and verified by human experts.

Maximizing the product of addends with a given sum. So we now have a one-variable function. That means the product is maximum, then X is equals to spy two. We'd have then that F of just X now is going to be X times actually was a capitalist, their X times s minus X or fx equals X S minus x squared.

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