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**1. Homework Statement**

A cylindrical can is to hold 500 cm^3 of apple juice the design must take into account that the height must be between 6 and 15 cm, inclusive. How should the can be constructed so that a minimum amount of material will be used in the construction? assume no waste.

**2. Homework Equations**

V is volume and SA is surface area

V= (pi)r^2h

SA=2(pi)rh + 2(pi)r^2

**3. The Attempt at a Solution**

so far this is what I have:

15>h>6

v=(pi)r^2h

500=(pi)r^2h

500/(pi)r^2=h

SA=2(pi)r(500/(pi)r^2) + 2(pi)r^2

Now I believe I need to find the derivative and set it to zero then solve for r.

The problem is that I can't quite figure out how I'm supposed to find the derivative if someone could give me a hand understanding the process I would really appreciate it as I have forgotten and my teacher is busy with the latest stuff.

Thanks,

~RS