# Rate of change from 1 to 2 for f(x)=2x^3 + x

by Rusho
Tags: fx2x3, rate
 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] / 2-1 = 2-1-2x^3 + x / 1 = 1-2x^3 + x = -2x^3 + x Right?
 Sci Advisor HW Helper P: 2,002 The average rate of change of f from a to b is [f(b)-f(a)]/(b-a) and it's (naturally) just a number. It doesn't depend on x. Check your definition.
 P: 24 [2(2)^3 - 2(1)^3] - [2x^3 + x] / 2-1 16-1-2x^3 + x / 1 15-2x^3 + x I don't understand what you are telling me
 Sci Advisor HW Helper P: 2,002 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))/(2-1). By definition, the average rate of change of f on the interval [a,b] is: $$\frac{f(b)-f(a)}{b-a}$$ So in your case, the average rate of change is: $$\frac{f(2)-f(1)}{2-1}$$
 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 / 2-1 but the "+x" is confusing me
 P: 24 I think I got it 2(2)^3 + x - 2(1)^3 + x / 2-1 =16-2+x+x / 1 =14+2x =-2x + 14 x = -7
 Sci Advisor HW Helper P: 2,002 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)?
HW Helper
P: 2,278
 Quote by Rusho I think I got it 2(2)^3 + x - 2(1)^3 + x / 2-1 =16-2+x+x / 1 =14+2x =-2x + 14 x = -7
Calculate f(2). Calculate f(1). Subtract the result of f(1) from f(2).

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:

$$(3x^2 + 3x) - (2x^2 + 2x)$$
then the minus sign means both the 2x^2 and the 2x are negative:
$$3x^2 + 3x - 2x^2 - 2x$$
$$(3x^2 - 2x^2) + (3x - 2x)$$
etc.
 P: 24 2(2)^3 + (2) -1 / 2-1 16+2-1 / 2-1 17/1 17 I'm sorry if I'm just not getting it
 Sci Advisor HW Helper P: 2,002 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)]/(2-1) 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)]/(2-1)
 P: 24 2(2)^3 + (2) - 2(1)^3 +1 / 2-1 =18-3 / 2-1 =15/1 =15
 Sci Advisor HW Helper P: 2,002 Right that's correct. BTW: Mind your brackets: -2(1)^3+1 is not the same as -(2(1)^3+1)
 P: 24 Great! Thanks for your help! I have another one, maybe I should start a new post

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