anonymous
  • anonymous
Find the relative rate of change fro each of the following functions. f(x)=x^3 -3x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think you have to derive here, or am I wrong? Since it's about rate of change, right?
anonymous
  • anonymous
no this is the problem
anonymous
  • anonymous
the derivative would be 3x^2 -6x

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anonymous
  • anonymous
exactly
anonymous
  • anonymous
that's how you compute the relative rate of change, by deriving ^_^
anonymous
  • anonymous
im not understanding?
anonymous
  • anonymous
so do i take f'(x) and divide it by f(x)
anonymous
  • anonymous
lol, to find the relative rate of change, you have to find the derivative of the following function which is in this case :\[f(x) = x^3 - 3x^2\] so when you derive the function you'll get like what you've said : \[f'(x) = 3x^2 - 6x\] since there is no given for x, then that's the final equation I guess :)
anonymous
  • anonymous
if they told you, for example, that x = 2 then substitute it in the derived function and you'll find the relative rate of change
anonymous
  • anonymous
^_^ clearer?
anonymous
  • anonymous
or am I mixing it up with something?
anonymous
  • anonymous
i got all that, but my teacher still counted 2 points off?
anonymous
  • anonymous
hmm, I'm missing a point aren't I?
anonymous
  • anonymous
sstarica, when you're done here, can you help dinaortega? I'm leaving soon.
anonymous
  • anonymous
I'll try my best loki :)
anonymous
  • anonymous
could you help me lokisan?
anonymous
  • anonymous
Thanks.
anonymous
  • anonymous
np
anonymous
  • anonymous
relative rate of change is f'(x)/f(x)
anonymous
  • anonymous
>_< thank you blexting
anonymous
  • anonymous
blexting so how do i get that from f(x)= x^3 -3x^2 being the original problem and f'(x)=3x^2 -6x
anonymous
  • anonymous
Sorry.. I don't know, but I knew the formula.. sstarica can you help?
anonymous
  • anonymous
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anonymous
  • anonymous
divide f'(x) with f(x)
anonymous
  • anonymous
and simplify
anonymous
  • anonymous
x^3-6x?
anonymous
  • anonymous
6x/x^3
anonymous
  • anonymous
\[\frac{f'(x)}{f(x)}=\frac{3x^2-6x}{x^3-3x^2}=\frac{3x-6}{x^2-3x}\]
anonymous
  • anonymous
so you'll get :\[f'(x)/f(x) = (3x^2-6x)/(x^3-2x^2)\]\[= 3x(x-2)/x^2(x-2)\] \[= 3/x\]
anonymous
  • anonymous
right?
anonymous
  • anonymous
sstarica.. the original was 3x^2. I agree with lokisan
anonymous
  • anonymous
oh , sorry my bad ^^"
anonymous
  • anonymous
is it clearer now ballards?
anonymous
  • anonymous
thank you guys that makes since, but what if you have a log problem like this... f(x)=5x-xlnx
anonymous
  • anonymous
it is clear how to figure out the relative rate of change. Could someone help me figure out the f'(x) of that log then i maybe could get it from there
anonymous
  • anonymous
if f(x)=ln(x) f'(x)=1/x
anonymous
  • anonymous
same story, find the derivative then divide it by the original function ^_^ and you'll get : f'(x) = 5 - [lnx + 1] ( use u'v + uv' to find the derivatice of xlnx) then divide it by the original : \[f'(x)/f(x) = (5-\ln|x|-1)/ 5x - xlnx\] and try to simplify :) give it a try now.

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