Answer:
- The derivative when x = 3 mm is 27.
V'(3) = 27
- This means that the volume's rate of change when x = 3 (when the sides are 3mm) is 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,
<em>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. </em>