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hiramoby

  • 2 years ago

Find all relative extrema of the function F(X)=16/(X^2+1). Use the Second-Derivative Test when applicable. Answer a. The relative maximum is .1,0 b. The relative minimum is .0,1 c. The relative maximum is .0,16 d. The relative minimum is .0,16 e. The relative maximum is .16,0

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  1. Australopithecus
    • 2 years ago
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    Take the derivative of this function first

  2. hiramoby
    • 2 years ago
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    here we go

  3. Australopithecus
    • 2 years ago
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    First set f'(x) = 0 then solve for x, those will give you your critical points

  4. hiramoby
    • 2 years ago
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    I got 0

  5. hiramoby
    • 2 years ago
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    -32

  6. Australopithecus
    • 2 years ago
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    also make sure to check the domain of f'(x) and the domain of f(x) if something is not in the domain of f'(x) but is in the domain of f(x) then it is a critical point if a point is not in the domain of f(x) but is in the domain of f'(x) then it is not a critical point

  7. hiramoby
    • 2 years ago
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    so it is going to be e then

  8. Australopithecus
    • 2 years ago
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    ok make a table |dw:1351050419295:dw|

  9. Australopithecus
    • 2 years ago
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    check in between these numbers and right if they are positive or negative

  10. hiramoby
    • 2 years ago
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    no b is the answer

  11. Australopithecus
    • 2 years ago
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    you need to check to see if they are maximums or minimums

  12. Australopithecus
    • 2 years ago
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    and I'm showing you how

  13. Australopithecus
    • 2 years ago
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    Oh I made a mistake the table should be |dw:1351050692097:dw| so the general rule is 1. If f'(x) > 0 on the Interval than f(x) is increasing on the interval 2. If f'(x) < 0 on the Interval than f(x) is decreasing on the interval

  14. Australopithecus
    • 2 years ago
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    So to show you an example of this -32x/(x^4 + 2x^2 + 1) sub in a number in the interval (-infinity, 0) so I'm going with -1 -32(-1)/((-1)^4 + 2(-1)^2 + 1) = a positive number so we add in the table |dw:1351050909010:dw|

  15. Australopithecus
    • 2 years ago
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    then we do it again for the next interval (0, -32) so I will pick 1 f'(1) = -32(1)/((1)^4 + 2(1)^2 + 1) = a negative number |dw:1351051038432:dw| so we see from this table that 0 is a maximum

  16. Australopithecus
    • 2 years ago
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    I mean minimum

  17. Australopithecus
    • 2 years ago
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    we can insert 0 into f(x) to see where this minimum is f(0) = 16/(X^2+1) f(0) = 16/1 f(0) = 16 so we have a minimum at (0,16)

  18. Australopithecus
    • 2 years ago
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    I hope this was helpful :S

  19. Australopithecus
    • 2 years ago
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    oh crap made a mistake lol |dw:1351051431080:dw| it should be this you are right it is e maximum at (0,16)

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