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?