SOLUTION: The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first pri

Question 868034: The volume of grains in a silo at a particular time (measured in hours) is given
by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the
silo from first principles (using the definition of the rate of change).
Found 3 solutions by Fombitz, stanbon, Ra:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

You have a mistake here,

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
My answer is:
V(t)=4t(3-t)
Rate of change of volume of V(t) is V'(t)
V(t)=4t(3-t)
-------------------------
V(t) = 12t-4t^2
-------------------------
V(t+D) = 12(t+D) - 4(t+D)^2
= 12t+12D -4(t^2+ 2tD + D^2)
= 12t +12D -4t^2 -8tD -4D^2
-------------------------------------------
[V(t+∆t)- V(t)] / ∆t
= [ 12D - 8(tD) -4(D)^2]/D
= [12 - 8t - 4D]
lim of V(t)/Dt as V goes to 0 = 12-8t
================
Cheers,
Stan H.
===============

Answer by Ra(1)   (Show Source): You can put this solution on YOUR website!
So you can use the power rule which is easier, if ur tutor doesnt want u to show all work. using the formula like the other guys.

so

Heaps easier!!!
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