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Hello, I'm a bit stuck on one question and was wondering if anyone could help:

The total surface area of a cylinder A cm^2 with a fixed volume of 1000 cubic cm is given by the formula A = 2PIx^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 zrero,

x^3 = 500/PI

Now, I don't know what I am doing wrong, but I am differentiating the

A = 2PIx^2 + 2000/x equation. and I get x= 500/PI (instead of x^3).

Also I don't know if the number 1000 is relevant at all to answer the actual question.

Thank you.

(I am sure I just missed something, I just can't see it...)

The total surface area of a cylinder A cm^2 with a fixed volume of 1000 cubic cm is given by the formula A = 2PIx^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 zrero,

x^3 = 500/PI

Now, I don't know what I am doing wrong, but I am differentiating the

A = 2PIx^2 + 2000/x equation. and I get x= 500/PI (instead of x^3).

Also I don't know if the number 1000 is relevant at all to answer the actual question.

Thank you.

(I am sure I just missed something, I just can't see it...)

Swordsikan

Hello, I'm a bit stuck on one question and was wondering if anyone could help:

The total surface area of a cylinder A cm^2 with a fixed volume of 1000 cubic cm is given by the formula A = 2PIx^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 zrero,

x^3 = 500/PI

Now, I don't know what I am doing wrong, but I am differentiating the

A = 2PIx^2 + 2000/x equation. and I get x= 500/PI (instead of x^3).

Also I don't know if the number 1000 is relevant at all to answer the actual question.

Thank you.

(I am sure I just missed something, I just can't see it...)

The total surface area of a cylinder A cm^2 with a fixed volume of 1000 cubic cm is given by the formula A = 2PIx^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 zrero,

x^3 = 500/PI

Now, I don't know what I am doing wrong, but I am differentiating the

A = 2PIx^2 + 2000/x equation. and I get x= 500/PI (instead of x^3).

Also I don't know if the number 1000 is relevant at all to answer the actual question.

Thank you.

(I am sure I just missed something, I just can't see it...)

A = 2pix^2 + 2000/x

A = 2pix^2 + 2000x^-1

dA/dx = 4pix - 2000x^-2

dA/dx = 4pix - 2000/x^2

when the rate of change of the area with respect to the radius is zero, dA/dx = 0

=> 4pix - 2000/x^2 = 0

4pix = 2000/x^2

4pix^3 = 2000

x^3 = 2000/4pi = 500/pi

ok, thank you. I've seen where I went wrong.

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