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ksandoval

  • 3 years ago

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

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  1. ksandoval
    • 3 years ago
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    and i know that the derivative is f'(x) = -1/x^2 + 1/x but i dont know where to go from there... lol

  2. baldymcgee6
    • 3 years ago
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    Where do extreme values occur?

  3. ksandoval
    • 3 years ago
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    i dont know thats what i need help finding.. lol. i just dont know how to find them.

  4. baldymcgee6
    • 3 years ago
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    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.

  5. ksandoval
    • 3 years ago
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    okay sooo i set the derivative equal to zero...

  6. baldymcgee6
    • 3 years ago
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    and...?

  7. ksandoval
    • 3 years ago
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    well i mean plugging in 1 for x would give you zero.

  8. baldymcgee6
    • 3 years ago
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    okay, so 1 is one of our critical points

  9. ksandoval
    • 3 years ago
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    now what do we do?

  10. baldymcgee6
    • 3 years ago
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    Where is f'(x) = -1/x^2 + 1/x undefined?

  11. ksandoval
    • 3 years ago
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    when x = 0?

  12. baldymcgee6
    • 3 years ago
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    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

  13. baldymcgee6
    • 3 years ago
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    http://screencast.com/t/LJnPiplk

  14. ksandoval
    • 3 years ago
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    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?

  15. baldymcgee6
    • 3 years ago
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    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.

  16. baldymcgee6
    • 3 years ago
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    there is no local max... so i'm not sure where they got that.. might want to ask your teacher.

  17. ksandoval
    • 3 years ago
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    oh.. ok. and how do they know that 1 is the min value? this is confusing for me ):

  18. baldymcgee6
    • 3 years ago
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    We already got that the minimum is at x = 1

  19. ksandoval
    • 3 years ago
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    yea but how do you know its the minimum? :\

  20. baldymcgee6
    • 3 years ago
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    We know it is the minimum because at that point, the derivative = 0, this is the lowest point on the curve.

  21. ksandoval
    • 3 years ago
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    thank you

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