The volume of a cube is changing at a rate of 18 cubic cm/second. How fast is the edge of the cube expanding when each edge is a)2cm and b)3cm. Any help appreciated.Thanks
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Let x = length of the side of the cube. Volume of a cube is $\displaystyle v(x)=x^3$, therefore $\displaystyle dv/dx = 3x^2$. Therefore when $\displaystyle x = 2$, $\displaystyle dv/dx = 12 $, and when $\displaystyle x = 3$, $\displaystyle dv/dx = 27$.
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