Suppose you have a cube of length s. the volume of that cube is v = s^3. now let's suppose the dimensions of that cube (and hence its volume) depend on time. we are wondering about the relationship between the growth of the length versus the growth of the volume. suppose

s(t) = t.

then

s'(t) = and v'(t) = t

next suppose v(t) = t.

s'(t) = and v'(t) =

Part 1

s'(t)=1

Part 2

V'(t)=1

Step-by-step explanation:

As stated in the question, if s is the length of a cube, its volume is

When s changes in time, the volume will change too. The challenge here is to find the growth of the volume in terms of those changes in length

Part 1

The change of s with respect to time is found by differentiating the relation to get

The volume will also change, and its derivative is

Since s'=1

How s=t

Part 2

Replacing this into the formula for V(s)

So we have

Computing the derivatives:

V(t)=t =>

V'(t)=1

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation: