Not sure what section this is from

[whiteti]

I missed a class, and this question is surprising me:

Find two positive real numbers whose sum is 100 and whose product is a maximum.

uhh? help!

 

[srmichael]

I missed a class, and this question is surprising me:

Find two positive real numbers whose sum is 100 and whose product is a maximum.

uhh? help!

This is from the Optimization section of calculus. Unfortunately, this forum is not the place where we teach an entire concept to someone who may have missed that topic in class. I suggest you ask your teacher for further clarifiaction or, at the very least, Google Calculus Optimization and you will get many very helpful sites.

 

[pka]

I missed a class, and this question is surprising me:

Find two positive real numbers whose sum is 100 and whose product is a maximum.

Maximize \(\displaystyle M={(100-x)}{(x)}\).

 

[whiteti]

This is from the Optimization section of calculus. Unfortunately, this forum is not the place where we teach an entire concept to someone who may have missed that topic in class. I suggest you ask your teacher for further clarifiaction or, at the very least, Google Calculus Optimization and you will get many very helpful sites.

Thanks! Ill check out the optimization section and post again if im still stuck

 

[Deleted member 4993]

You should be able to answer this by thinking a bit.

What is the value of x, for f(x) = 100*x - x² to be maximum?

How do you find the maximum of a function?

 

[stapel]

I missed a class, and this question is surprising me:

Then use what you learned back in algebra!

Find two positive real numbers whose sum is 100 and whose product is a maximum.

Pick a variable for one of the numbers. Create an expression for the other number, using the fact they give you about the sum. Then create the "maximum" equation in terms of that variable. Then find the vertex.

Note: Unless you've missed a week or two of classes, you should be at least somewhat familiar with finding max/min points using derivatives. If you're needing lesson instruction on that whole topic (which you seem to be indicating), then please follow the advise provided earlier about speaking with your instructor and/or doing some self-study, such as with a private tutor or from online lessons such as this one.

 

[whiteti]

hello again,

I got:

Let x and y be the numbers, then xy=A and x+y=100
y=100-x => A(x)=x(100-x) = 100x-x²
A'(x)=100-2x => 100-2x=0

x= 50
A''(x) = -2
y=100-50=50

x= 50 and y = 50

is this correct?

 

[srmichael]

hello again,

I got:

Let x and y be the numbers, then xy=A and x+y=100
y=100-x => A(x)=x(100-x) = 100x-x²
A'(x)=100-2x => 100-2x=0

x= 50
A''(x) = -2
y=100-50=50

x= 50 and y = 50

is this correct?

Yup! And the fact that the second derivative is negative for all values of x proves that x = 50 produces a maximum product.