Could somebody help me w/ a step-by-step walkthrough of this unit that we're learning in school. Our math teacher doesn't teach us anything, and I want actual help from somebody who can help us properly as this year is necessary for my good grades to get into a good college.
Question:
Given that xy = 3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x + 3y/5.
Thanks so much, as I really need and geniunly want to understand this topic.
+129852 xy = 3/2 implies that y = 3 / [ 2x]
So....plugging this into the second function and get that
10x + (3/5)(3/[2x]) =
10x + 9 / (10x)
If you haven't had Calculus....we can find the minimum of this curve : https://www.desmos.com/calculator/nbecr6spbo
The minimum value occurs at x = 3/10 and the minimum is y = 6
If you have had Calculus....let the function be
y = 10x + (9/10)x^(-1) take the derivative and set to 0
y ' = 10 - (9/10)x^(-2) = 0
10 = (9/10)x^(-2) rearrange as
x^2 = 9/100 take the positive root (since x must be positive)
x = 3/10
Taking the second derivative we have
y " = (18/10)x^(-3)
Putting 3/10 into this produces a positive.....this indicates a minimum at x = 3/10
And y = 10(3/10) + (9/10)/ (3/10) =
3 + (9/10) (10/3) =
3 + 9/3 =
6 !!!
+118673 Chris you have answered the question for this person but it is highly unlikely that you have taught them anything.
You can not teach a person if you do not intereract with them.
I was about to answer when I saw you answering.
But my initial response would have been
Have you done any calculus yet?
And can you make y the subject for me (with the first expression) and then plug that y value into the second expression.
Get back to me when you have done that and we will continue furthed. 
I had an extremely frustrated teacher write a comprehsive message to me recently saying that we were destryoying his teaching world by supplying full cheat answers to his students.
I could understand his frustration. This forum has become best known as a cheat site. Sad but true.
