# Calculus Word Problem

Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If $V$ is the volume of such a cube with side length $x$, calculate the derivative when $x = 4 \text{ mm}$.

$$V'(4) = \cdots \text{ mm}^3/\text{mm}$$

I thought that:

$$V'(4) = 64 \text{ mm}^3/\text{mm}$$

Because volume of a cube $=$ $4 \times 4 \times 4$

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In your first equation, what is the "?" supposed to represent? I think if you replace that with the correct derivative of V(x), you'll be able to find your answer. Just to be clear: write the equation for the volume of a cube with side length x, then take the derivative of that equation, then plug in 4. – Todd Wilcox Oct 22 '12 at 4:19
an unknown number – dsta Oct 22 '12 at 4:20
I don't have an equation. – dsta Oct 22 '12 at 4:21
Try searching the internet or your calculus book for equation for the volume of a cube. – Todd Wilcox Oct 22 '12 at 4:21
So the answer would be 48. Thank you!!! – dsta Oct 22 '12 at 4:23

$V(x)=x^3$ is the volume of a cube with side $x$. Take the derivative of that to get $V'(x)$ and then calculate $V'(4)$.