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 = 3 mm and explain its meaning.

         V'(3) = 27

Step-by-step explanation:

The volume of a cube with side length x can be expressed as:

for a cube: ×

-Since the side length is x then:

The derivative of V is:

-When x = 3 the derivative is:

-Therefore,

Keep in mind that a derivative represents the slope of the tangent line at a given point. It can also mean the rate of change at which the volume is changing when the side lenght is 3.