anonymous
  • anonymous
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.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
We can factor out the denominator as follows (x+2)(x-2)
anonymous
  • anonymous
2,-2 are your verticle retricemtote
anonymous
  • anonymous
how to find the domain and point of inflection

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anonymous
  • anonymous
domain is everywhere except 2,-2 For inflection point and extrema you will need to take derivative of the function
anonymous
  • anonymous
Do you know how to take derivative?
anonymous
  • anonymous
yes then after taking derivative what shall i do
anonymous
  • anonymous
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
anonymous
  • anonymous
derivative is ((x^2-4)(2x)-(x^2+1)(2x))/(x^2-4)^2
anonymous
  • anonymous
so i equated it to zero..
anonymous
  • anonymous
from which i get x=0
anonymous
  • anonymous
then what shall I do?
anonymous
  • anonymous
Then the extrema is at x=0
anonymous
  • anonymous
you can find the inflection point
anonymous
  • anonymous
it says to find local extrema is that the local extrema value.
anonymous
  • anonymous
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.
anonymous
  • anonymous
time traveler?

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