# 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 $=$ $4 \times 4 \times 4$

• 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. Oct 22, 2012 at 4:19
• an unknown number
– dsta
Oct 22, 2012 at 4:20
• I don't have an equation.
– dsta
Oct 22, 2012 at 4:21
• Try searching the internet or your calculus book for equation for the volume of a cube. Oct 22, 2012 at 4:21
• So the answer would be 48. Thank you!!!
– dsta
Oct 22, 2012 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 $V'(4)$.