anonymous
  • anonymous
use analytic methods to find the extreme values of f(x)= (1/x) + lnx on the interval 0.5 ≤ x ≤ 4 and where they occur
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
and i know that the derivative is f'(x) = -1/x^2 + 1/x but i dont know where to go from there... lol
baldymcgee6
  • baldymcgee6
Where do extreme values occur?
anonymous
  • anonymous
i dont know thats what i need help finding.. lol. i just dont know how to find them.

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baldymcgee6
  • baldymcgee6
okay, so in theory, extreme values will occur where the derivative of the function is equal to zero (i.e. a horizontal slope where there is maxima or minima), and they also occur where the derivative is undefined.
anonymous
  • anonymous
okay sooo i set the derivative equal to zero...
baldymcgee6
  • baldymcgee6
and...?
anonymous
  • anonymous
well i mean plugging in 1 for x would give you zero.
baldymcgee6
  • baldymcgee6
okay, so 1 is one of our critical points
anonymous
  • anonymous
now what do we do?
baldymcgee6
  • baldymcgee6
Where is f'(x) = -1/x^2 + 1/x undefined?
anonymous
  • anonymous
when x = 0?
baldymcgee6
  • baldymcgee6
exactly, but if you would notice in the question it gave us restrictions of 0.5 ≤ x ≤ 4, so we dont take 0 into account... So our critical point is 1
baldymcgee6
  • baldymcgee6
http://screencast.com/t/LJnPiplk
anonymous
  • anonymous
oooh ok. so for the answer it says: max value is 1/4 + ln4 at x = 4 min value is 1 at x = 1 local max at (1/2, 2 - ln2) how did they get the max value and local max?
baldymcgee6
  • baldymcgee6
Well for the max value, they just put the biggest number they could, 4, into the function, they chose 4 because of the restrictions 0.5 ≤ x ≤ 4... 4 is the biggest number, i.e. giving the biggest value.
baldymcgee6
  • baldymcgee6
there is no local max... so i'm not sure where they got that.. might want to ask your teacher.
anonymous
  • anonymous
oh.. ok. and how do they know that 1 is the min value? this is confusing for me ):
baldymcgee6
  • baldymcgee6
We already got that the minimum is at x = 1
anonymous
  • anonymous
yea but how do you know its the minimum? :\
baldymcgee6
  • baldymcgee6
We know it is the minimum because at that point, the derivative = 0, this is the lowest point on the curve.
anonymous
  • anonymous
thank you

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