00:01
The value of a machine after t years of service is given by v of t.
00:06
And my v of t here is equal to 100 t squared minus 3 ,000 t plus 20 ,000.
00:19
We want to know at what rate does the machine depreciate after five years.
00:26
If i'm looking for an instantaneous rate of change, i need my derivative.
00:32
I need v prime of t.
00:37
How do i take the derivative of 100 t squared? well, i take my exponent 2, and i multiply it down to the front.
00:49
200, and then i subtract one from the exponent, so i get 200t to the first power.
00:58
The derivative of 100 t squared is 200t, minus, then i need the derivative of 3 ,000 t.
01:11
The derivative of any constant times t is just that constant...