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C1 - Differentiation

I'm having a little difficulty with these:

1) The volume Vcm^3, of a tin of radius r cm is given by the formula V=pi(40r-r^2-r^3). Find the positive value of r for which dV/dr=0, and find the value of V which corresponds to this value of r.

2) The total surface area of a cylinder Acm^2 with a fixed volume of 1000 cubic cm is given by the formula A=2(pi)x^2+2000/x, where x cm is the radius. Show that when the rate of change of the area with respect to the radius is zero, x^3=500/pi

3) The curve with equation y=ax^2+bx+c passes through the point (1,2). The gradient of the curve is zero at the point (2,1). Find the values of a, b & c.

I hate these wordy questions. :frown:
Reply 1
For the first one you will want to expand the bracket and then differentiate, remember that pi is just a number.
Original post by najinaji
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Reply 2
Original post by TheJ0ker
For the first one you will want to expand the bracket and then differentiate, remember that pi is just a number.

I tried that, and this is my result:

dV/dr = 40(pi) - 2r(pi) -3r^2(pi)

40 - 2r - 3r^2/pi

I'm not really sure where to go from there.
Reply 3
from dV/dr = 40(pi) - 2r(pi) - 3r^2(pi),

set dV/dr =0,

So, 40(pi) - 2r(pi) - 3r^2(pi)=0.

take out pi as a factor, and solve the remaining quadratic for r.

as the question asks for the positive value of r, choose the appropriate one and sub it back in to the original equation to find V.
Reply 4
Original post by Tomming
from dV/dr = 40(pi) - 2r(pi) - 3r^2(pi),

set dV/dr =0,

So, 40(pi) - 2r(pi) - 3r^2(pi)=0.

take out pi as a factor, and solve the remaining quadratic for r.

as the question asks for the positive value of r, choose the appropriate one and sub it back in to the original equation to find V.

Excellent, thank you! :biggrin:
Reply 5
No problem, do you still need some help with the others?

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