Question

Calculus: Is this correct?
All edges of a cube are expanding at a rate of 6 cm/sec. How fast is the volume changing when each edge is 2 cm?
V=x^3
V'=3x^2(x')
V(2)=3(2cm)^2(6cm/sec)
V(2)=72cm^3/sec

I am not sure I did this correctly, but I think I did...

Answer 1

V = (x(0)+vt)^3
if x(0) =0 then
V=(vt)^3=2^3
V'=3(vt)^2 v
V'=3(2)^2 6=72

Answer 2

I don't have a great understanding of this. Can you explain a little? This looks like you are refuting my answer?

Answer 3

I think I got it... There should be a multiplication between ^2 and your 6?

Answer 4

Eq 1 is volume with arbitrary initial side length
Eq 2 say's initial side length 0
Eq 3 is resulting volume at side length 2
Eq 4 takes the derivative of volume, v is constant therefore v' is 0
Eq 5 place result of Eq 3 and solved

Answer 5

I think you did too.

Answer 6

Thanks guys!