# Math Help - Couple of differentiation questions

1. ## Couple of differentiation questions (have added second problem)

Hi, I'm a bit stuck on a couple of things.

And the second one:
The diagram shows part of the curve with equation y=f(x)
It's basically an N shaped quadratic with a maximum at B. The curve cuts the x-axis at the points A and C.
f(x) = 200 - (250/x) - x^2, x>0
Find f'(x) I've done this, 250x^-2 -2x
Use this answer to calculate the co-ordinates of B.
I'm not really sure what to do. Usually these kind of things would factorise?

First question: HAVE SORTED THIS NOW, THANKS!
A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm. The radii of the tin and the lid are both x cm. The tin and the lid are made from a thin sheet of metal of area 80pi cm^2 and there is no wastage. The volume of the tin is V cm ^3.
Part
a) is show that V = pi(40x-x^2-x^3)
which I've done.
b) use differentiation to find the positive value for which V is stationary. I've got this to be 10/3, which I think is right.
c) Prove that this gives a maximum value of V.
I've done this ok, too.
d) Find this maxium value of V. I'm probably being really stupid, but this is the bit I can't do. I've tried a couple of things but I'm not coming out with the right answer.
e) The last bit is 'determine the percentage of the sheet metal used in the lid when V is a maximum'. Also not sure where to start with this. Can anyone give me any pointers?

2. Originally Posted by Selene
Hi, I'm a bit stuck on a couple of things.

First question:
A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm. The radii of the tin and the lid are both x cm. The tin and the lid are made from a thin sheet of metal of area 80pi cm^2 and there is no wastage. The volume of the tin is V cm ^3.
Part
a) is show that V = pi(40x-x^2-x^3)
which I've done.
b) use differentiation to find the positive value for which V is stationary. I've got this to be 10/3, which I think is right.
c) Prove that this gives a maximum value of V.
I've done this ok, too.
d) Find this maxium value of V. I'm probably being really stupid, but this is the bit I can't do. I've tried a couple of things but I'm not coming out with the right answer.
e) The last bit is 'determine the percentage of the sheet metal used in the lid when V is a maximum'. Also not sure where to start with this. Can anyone give me any pointers?
For d) substitute the x-value you found gives the maximum into the equation $V = \pi(40x - x^2 - x^3)$

3. Ah, yep. Done them both now! Got (2300pi)/27 and 22 2/9 % for e.
Was having a bit of a moment!