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Mathematics 21 Online
OpenStudy (anonymous):

Stuck- completely stuck!! Find the average rate of change of f(x)=x^3-3x^2+2x from x=-3 to x=2 I'm using this formula: (f(b)-f(a)) / (b-a) Can someone please assist?

OpenStudy (anonymous):

The third variable is throwing me off If I just had the f(x)=x^3-3x^2 I could probably figure it, but the additional +2x has be baffled

OpenStudy (experimentx):

... the problem is pretty straight forward.

OpenStudy (experimentx):

find b-a, b= 2 and a=-3

OpenStudy (anonymous):

I got a= -6 and b=0 Not sure if I did it right though

OpenStudy (experimentx):

huh ... did you read my second post?? read it again and check your result.

OpenStudy (anonymous):

It can't be as simple as -1 could it?

OpenStudy (anonymous):

I plugged in the equation f(-3)=(-3)^3-(3)(-3)^2+2(-3)=-6

OpenStudy (experimentx):

huh ... looks like you are confused again. it can't be -1

OpenStudy (anonymous):

b=(f(2)=(2)^3-(3)(2)^2+2(2)= 0

OpenStudy (experimentx):

you are terribly mistaken ... somwhere.

OpenStudy (experimentx):

you are checking f(x) between -3 and 2 so your x goes from -3 to 2 ... so a=-3 and b=2 ... when is b-a??

OpenStudy (anonymous):

lost. I'm not sure what you're asking. I'm using the average rate of change formula: (f(b)-f(a)) / (b-a) is that wrong

OpenStudy (experimentx):

find \[ \frac{f(2) - f(-3)}{2 - (-3)}\]

OpenStudy (anonymous):

I get -1/5

OpenStudy (experimentx):

then that is your result.

OpenStudy (anonymous):

So I don't continue with the function to solve?

OpenStudy (experimentx):

No ..

OpenStudy (anonymous):

That was incorrect...

OpenStudy (experimentx):

yes ... that was incorrect. because you did not calculate it correctly ... and i was too lazy to calculate it. http://www.wolframalpha.com/input/?i=Table%5Bx%5E3-3x%5E2%2B2x%2C+%7Bx%2C+-3%2C+2%7D%5D

OpenStudy (anonymous):

Thank you X!

OpenStudy (experimentx):

You are welcome. the answer is -12

OpenStudy (anonymous):

I'm still working through the steps. I see the table but I just can't wrap my head around getting to the answer -12. I've watched numerous youtube videos: http://www.youtube.com/watch?v=Z2v6WvReCzg where they step it out...

OpenStudy (anonymous):

f(x) or 'a' = x^3-3x^2+2x,[ x=-3] f(x) or 'b'= x^3-3x^2+2x, [x=2] plugging in the values -3, and 2 a= -60 b= 0 equation looks like this \[-60-0/2-(-3)= -60/5 \]

OpenStudy (experimentx):

yeah ... that's right direction.

OpenStudy (anonymous):

which simplifies to -12 Sorry X- couldnt understand or get passed the tables on wolframs

OpenStudy (experimentx):

f(-3) = -60 and f(2) = 0 that's why i showed you that table. now you understand it ... it's good.

OpenStudy (anonymous):

but if it is f(b) - f(a) shouldn't u be getting answer +12?

OpenStudy (anonymous):

When I plugged it into a calculator I got positive 12 as well http://www.zweigmedia.com/ThirdEdSite/Calcsumm3.html

OpenStudy (anonymous):

+12 is the answer then,i guess

OpenStudy (anonymous):

But when I factored it out from the table that X gave me I got -60/5 which equals -12.

OpenStudy (anonymous):

hmm....i dunno then...

OpenStudy (anonymous):

but according to the formula i guess it should be +12 where is experimentX though?

OpenStudy (anonymous):

dont know

OpenStudy (experimentx):

this is asking you to find \[ \frac{\int_a^bf'(x) dx }{b-a}\] which is equivalent to the formula you mentioned.

OpenStudy (experimentx):

woops!! looks like i make mistake of swapping 'a' an 'b' +12 is correct

OpenStudy (anonymous):

So you found the derivitive and solved it that way first.

OpenStudy (experimentx):

No no ... i forgot a was 2 and b was -3 ... on the numerator http://www.wolframalpha.com/input/?i=Integrate%5BD%5Bx%5E3-3x%5E2%2B2x%2C+x%5D%2C+%7Bx%2C+-3%2C2%7D%5D%2F5

OpenStudy (experimentx):

sorry ... i never checked answer. just guessed it.

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