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differentiation probelm

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?
Show YOUR working. We already know how to do it.
Reply 2
Avatar for madfish
madfish
OP
Original post by Mr M
Show YOUR working. We already know how to do it.


i don't have any working to show, our else I would


i am unsure of where to start
Reply 3
Avatar for Albino
Albino
11
Original post by madfish
i don't have any working to show, our else I would


i am unsure of where to start


x+y=5
Original post by madfish
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.
Reply 5
Avatar for madfish
madfish
OP
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?:colondollar:
Reply 6
Avatar for TenOfThem
TenOfThem
18
Original post by madfish
done, now what?:colondollar:


You have a function in x that you wish to maximise

What do you do to find the maximum of a function
Original post by madfish
done, now what?:colondollar:


Provide your answer so far.

You need to differentiate now.
Reply 8
Avatar for madfish
madfish
OP
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
Original post by madfish
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 dPdx\frac{dP}{dx}
Reply 10
Avatar for madfish
madfish
OP
Original post by Mr M
Multiply through by x.

Now find dPdx\frac{dP}{dx}


okay so DP/DX = 5-2x then x=5/2
Original post by madfish
okay so dP/dx = 5-2x then x=5/2


Yes and what does y equal?
Reply 12
Avatar for madfish
madfish
OP
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?
Original post by madfish
I guess I sub in x to the original equation to get y?

y=0.5?


2.5+0.5≠52.5 + 0.5 \neq 5
Reply 14
Avatar for madfish
madfish
OP
Original post by Mr M
2.5+0.5≠52.5 + 0.5 \neq 5

x=y=2/5
Original post by madfish
x=y=2/5


0.4+0.4≠50.4 + 0.4 \neq 5
Reply 16
Avatar for madfish
madfish
OP
Original post by Mr M
0.4+0.4≠50.4 + 0.4 \neq 5

5/2!! damn sorry copied 2/5 down by mistake
Original post by madfish
5/2!! damn sorry copied 2/5 down by mistake


Yes that's right.

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