The volume of a cube with sides of length s is given by V =s^3. What is the rate of change of the volume with respect to s when s is 6 centimeters?

reiselivloy

reiselivloy

Answered question

2023-02-14

The volume of a cube with sides of length s is given by V = s 3 . What is the rate of change of the volume with respect to s when s is 6 centimeters?

Answer & Explanation

Sasha Bradley

Sasha Bradley

Beginner2023-02-15Added 4 answers

We are given the volume function:
V = s 3
The first derivative of this function is used to determine the rate of change. Because it provides the gradient of a tangent line drawn at the given location, this is frequently referred to as the gradient function.
d V d s ( s 3 ) = 3 s 2
We now plug in s = 6
3 s 2 = 3 ( 6 ) 2 = 108 c m 3 s

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