How do you use the formula V = l^3 for the volume of a cube of side l to find
(a) the average rate at which the volume of a cube changes with l as l increases from l = 2 to l = 4
(b) the instantaneous rate at which the volume of a cube changes with l when l = 5.

Question

How do you use the formula V = l^3 for the volume of a cube of side l to find
(a) the average rate at which the volume of a cube changes with l as l increases from l = 2 to l = 4
(b) the instantaneous rate at which the volume of a cube changes with l when l = 5.

amistre64 · Answer

define V at I=4 and I =2,  then divide the difference by 4-2

amistre64 · Answer

then define the derivative at I=5

amistre64 · Answer

why they want to define a side by I instead of s is beyond me:

a)$$\frac{4^3-2^3}{4-2}$$


b)$$V=s^3$$$$V'=3s^2$$

wesdg1978 · Answer

Thanks!

amistre64 · Answer

youre welcome