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anonymous

  • 5 years ago

analyze and sketch the graph of f(x)=(x^2+1)/(x^2-4). Write the domain, asymptotes, local extrema and inflection point if any.

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  1. anonymous
    • 5 years ago
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    We can factor out the denominator as follows (x+2)(x-2)

  2. anonymous
    • 5 years ago
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    2,-2 are your verticle retricemtote

  3. anonymous
    • 5 years ago
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    how to find the domain and point of inflection

  4. anonymous
    • 5 years ago
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    domain is everywhere except 2,-2 For inflection point and extrema you will need to take derivative of the function

  5. anonymous
    • 5 years ago
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    Do you know how to take derivative?

  6. anonymous
    • 5 years ago
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    yes then after taking derivative what shall i do

  7. anonymous
    • 5 years ago
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    The first derivative function F'[x], find out where it is zero; this is where extrema are located. For inflection point take derivative again F''[x], and find out where the function is zero; This is your inflction point

  8. anonymous
    • 5 years ago
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    derivative is ((x^2-4)(2x)-(x^2+1)(2x))/(x^2-4)^2

  9. anonymous
    • 5 years ago
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    so i equated it to zero..

  10. anonymous
    • 5 years ago
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    from which i get x=0

  11. anonymous
    • 5 years ago
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    then what shall I do?

  12. anonymous
    • 5 years ago
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    Then the extrema is at x=0

  13. anonymous
    • 5 years ago
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    you can find the inflection point

  14. anonymous
    • 5 years ago
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    it says to find local extrema is that the local extrema value.

  15. anonymous
    • 5 years ago
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    To find local extrema, create a number line from negative infinity to positive, investigate at critical points, the point where first derivative goes from pos to neg or vice versa: local extrema.

  16. anonymous
    • 5 years ago
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    time traveler?

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