Question

Maxim/Minimum Extrema derivatives
One model of worldwide oil production is the function given by the following formula where P(t) is the # of barrels in billions produced in a year, t years after 1933. According to this model, in what yaer did worldwide oil production achieve an absolute maximum? What was that maximum?

P(t)=0.0000000218t^4-0.0000167t^3+0.00156t^2+0.002t+0.22 0 12 years ago

Answer 1

where are you stuck at?

Answer 2

Evy part lol :X

Answer 3

Every**

Answer 4

ok ^_^

Answer 5

You have no idea how much you're saving me.. Nobody likes my questions:(

Answer 6

so every time the phrase 'minimum' or 'maximum' show up in a problem with an equation, it means we need to do the math operation of taking the derivative.
make senes?

Answer 7

Yes:-)

Answer 8

well, i might be creating problems for you in the end more than saving you, lol.

Answer 9

can you find the derivative of the equation given?

Answer 10

Is finding the derivative where you are stuck?
is this a calculs class or algebra?

Answer 11

I gotta go in 5 min, fyi

Answer 12

it's calc

Answer 13

Got it. (109t^3-62625t^2+3900000x+2500000)/1250000000

Answer 14

right idea, but the numbers are off
remember
0.0000000218t^4
would become
(4) * 0.0000000218 t^3
[you times the power to the front, and drop the power by 1]
try it again with this idea

Answer 15

O.o I have no idea. I dropped the powers?

Answer 16

ya, when you do the derivative, you take the power of what you have and times it down to the coefficient, then drop exponent from 4 to 3

Answer 17

I did though:( 4 went to 3 etc

Answer 18

hey, i got to take off, but i'd repost this question, but once you find the derivative of the equation you need to find the roots of all the t terms, these roots will give you either the minimum or the maximum.
also, there will be 3 roots.

Answer 19

@ranga

Answer 20

I will answer in a few minutes as I am typing replies to two other questions...

Answer 21

Take your time:-)

Answer 22

P(t) = 0.0000000218t^4-0.0000167t^3+0.00156t^2+0.002t+0.22

Take derivative one term at a time.

What is derivative of:

0.0000000218t^4
-0.0000167t^3
0.00156t^2
0.002t
0.22

Answer 23

0.0000000872t^3

Answer 24

-0.0000501t^2

Answer 25

0.00312t

Answer 26

and 0.002

Answer 27

Yes. Put them together and equate it to 0 and solve for t.

Answer 28

0.0000000872t^3-0.0000501t^2+0.00312t+0.002=0

I got three answers
t=71.8056
503.37
-0.634553

Answer 29

How did you solve the cubic equation? Calculator?

Assume those three values are correct, you can throw away -0.634553 because it is going back prior to the year 1933 and the equation is valid only after 1933.

You can also throw away 503.37 because it is centuries into the future and the model may not be valid that far into the future. So t=71.8056 is reasonable. Round it to t=72 years.

t is the measure of time since 1933. So add 72 to 1933 to find the year P(x) is maximum.

Substitute t = 72 in P(x) and find the maximum value.

Strictly speaking, you should also take a second derivative, put in t=71.8056 and prove it is a maxima. P''(t) should be negative for maxima.

Answer 30

Yes a calculator. And so my answer is 4.1billion barrels in 2005?

Answer 31

Or perhaps we should not round the year because adding 71.8 and 72 to 1933 will gives us the years 2004 or 2005. So the year will be off by 1.

So you can choose to keep t=71.8056 and say the year is 2004 and put
t=71.8056 in P9t) calculate the exact value.

I will have to take your word for it as to the three roots of the cubic equation and the 4.1 billion barrels because I don't have a scientific calculator.