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# differentiation probelm watch

1. the sum of two numbers x and y is constant and equal to 5

a) write down an expression for the product p of the two numbers in terms of x
b)hence find the values of x and y which maximise the product

any ideas?
3. (Original post by Mr M)
i don't have any working to show, our else I would

i am unsure of where to start
i don't have any working to show, our else I would

i am unsure of where to start
x+y=5
i don't have any working to show, our else I would

i am unsure of where to start
Write down the sum you are given in terms of x and y.

Make y the subject.

Write down the product you are given in terms of x and y.

Eliminate y in the product.

Report back when you have done this.
6. (Original post by Mr M)
Write down the sum you are given in terms of x and y.

Make y the subject.

Write down the product you are given in terms of x and y.

Eliminate y in the product.

Report back when you have done this.
done, now what?
done, now what?
You have a function in x that you wish to maximise

What do you do to find the maximum of a function
done, now what?

You need to differentiate now.
9. (Original post by TenOfThem)
You have a function in x that you wish to maximise

What do you do to find the maximum of a function
I get x+y=5 then p=xy

then p/x=5-x

not sure what to do now
I get x+y=5 then p=xy

then p/x=5-x

not sure what to do now
Multiply through by x.

Now find
11. (Original post by Mr M)
Multiply through by x.

Now find
okay so DP/DX = 5-2x then x=5/2
okay so dP/dx = 5-2x then x=5/2
Yes and what does y equal?
13. (Original post by Mr M)
Yes and what does y equal?
I guess I sub in x to the original equation to get y?

y=0.5?
I guess I sub in x to the original equation to get y?

y=0.5?
15. (Original post by Mr M)
x=y=2/5
x=y=2/5
17. (Original post by Mr M)
5/2!! damn sorry copied 2/5 down by mistake
5/2!! damn sorry copied 2/5 down by mistake
Yes that's right.

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