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Rate of change from 1 to 2 for f(x)=2x^3 + x 
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#1
Apr806, 06:50 AM

P: 24

Find the average rate of change from 1 to 2 for the function f(x)=2x^3 + x
so I did this: [f(2) – f(1)] – [2x^3 + x] / 21 = 212x^3 + x / 1 = 12x^3 + x = 2x^3 + x Right? 


#2
Apr806, 06:53 AM

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The average rate of change of f from a to b is
[f(b)f(a)]/(ba) and it's (naturally) just a number. It doesn't depend on x. Check your definition. 


#3
Apr806, 07:08 AM

P: 24

[2(2)^3  2(1)^3]  [2x^3 + x] / 21
1612x^3 + x / 1 152x^3 + x I don't understand what you are telling me 


#4
Apr806, 07:14 AM

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Rate of change from 1 to 2 for f(x)=2x^3 + x
You've got the definition of the average rate of change wrong.
You wrote something like (f(2)f(1)f(x))/(21). By definition, the average rate of change of f on the interval [a,b] is: [tex]\frac{f(b)f(a)}{ba}[/tex] So in your case, the average rate of change is: [tex]\frac{f(2)f(1)}{21}[/tex] 


#5
Apr806, 07:23 AM

P: 24

Ok, I am not sure what to do with 2x^3 + x . So I subtracted it from the f(b)  f(a).
If I had 2x^3 by it self, I can see just putting 2(2)^3  2(1)^3 / 21 but the "+x" is confusing me 


#6
Apr806, 07:53 AM

P: 24

I think I got it
2(2)^3 + x  2(1)^3 + x / 21 =162+x+x / 1 =14+2x =2x + 14 x = 7 


#7
Apr806, 07:57 AM

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So you can solve it if the function is 2x^3, but not if it's 2x^3+x? What's the difference, conceptually?
f(x)=2x^3+x, so what is f(2)? And what is f(1)? 


#8
Apr806, 09:36 AM

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The solution for f(2) is not 16+x. You have to substitute '2' for x everywhere it appears, so the solution for f(2) is 16+2. Also, your algebra is wrong (in addition to being not applicable in this case). If you have: [tex](3x^2 + 3x)  (2x^2 + 2x)[/tex] then the minus sign means both the 2x^2 and the 2x are negative: [tex]3x^2 + 3x  2x^2  2x[/tex] [tex](3x^2  2x^2) + (3x  2x)[/tex] etc. 


#9
Apr806, 10:05 AM

P: 24

2(2)^3 + (2) 1 / 21
16+21 / 21 17/1 17 I'm sorry if I'm just not getting it 


#10
Apr806, 10:49 AM

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Alright, let's take some steps back.
You are given a function f. It's a machine that eats a number and spits out a (usually different) number. f(x)=2x^3+x tells you the value of the function at each point, it's an equality that holds for each number x. For example: f(1)=2(1)^3+1=2+1=3 f(5)=2(5)^3+5=2(125)+5=255 So if you want to calculate [f(2)f(1)]/(21) you have to calculate f(2) and f(1). I already did f(1) for you above. Now you do f(2) and calculate [f(2)f(1)]/(21) 


#11
Apr806, 11:00 AM

P: 24

2(2)^3 + (2)  2(1)^3 +1 / 21
=183 / 21 =15/1 =15 


#12
Apr806, 11:29 AM

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Right that's correct.
BTW: Mind your brackets: 2(1)^3+1 is not the same as (2(1)^3+1) 


#13
Apr806, 12:32 PM

P: 24

Great! Thanks for your help!
I have another one, maybe I should start a new post 


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