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# Differentiation or Integration? watch

1. The point (-2,-1) lies on the graph of a function whose derivative f'(x) = 3x² - 12. Find f(x). I don't know exactly what I'm suppose to do with the points. I ended up with:

f(x) = x³ - 12x

That looks completely wrong and too simple. Any help would be appreciated.
2. You have started correctly but forgotten the constant of integration

you should have

Then use your given point to find c
3. You forget the "+ Constant of Integration"

You are told the point through which the graph passes, so you must now use this to find the exact value of this constant.
When integrating you always add c
5. (Original post by daisyclouds)
The point (-2,-1) lies on the graph of a function whose derivative f'(x) = 3x² - 12. Find f(x). I don't know exactly what I'm suppose to do with the points. I ended up with:

f(x) = x³ - 12x

That looks completely wrong and too simple. Any help would be appreciated.
You've got the right idea, but remember you have a constant when integrating something. So it'll be

Then use the values from the point to figure out c.

EDIT: Beaten to it by a fair few people - Maths forum is on top form tonight!
6. Don't forget to add a constant when you integrate.

You can use the point on the curve that they gave you to calculate c

EDIT: ...wow
7. remember when you integrate it becomes x3+12x + C <-- thats the important bit.

You can then work out C as you have the pints (-2 which is x and -1 which is the f(x))
f(x)=x^3-12x+c
put the two coordinates in

-1=-2^3 +24 + c

solve the equation to find out c and then put the c into the equation
8. Boy you peeps are slow

LoL

9. Don't forget to add the consta- oh forget it, the train has left the station, stopped at the end of the line and the driver is taking his lunch break.
10. so I substitute (-2,-1) into the equation:

-1 = (-2)³ - 12(-2) + c
-1 = -8 +24 + c
-1 = 16 + c
c = -17

meaning my final equation would be:

f(x) = x³ - 12x - 17 ?
11. (Original post by TenOfThem)
when you change that c to -17 yes
haha yeah just did (edit), my bad :P
12. (Original post by daisyclouds)
so I substitute (-2,-1) into the equation:

-1 = (-2)³ - 12(-2) + c
-1 = -8 +24 + c
-1 = 16 + c
c = -17

meaning my final equation would be:

f(x) = x³ - 12x - 17 ?
Looks good to me.

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Updated: November 27, 2011
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