Question

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.

Answer 1

We can factor out the denominator as follows
(x+2)(x-2)

Answer 2

2,-2 are your verticle retricemtote

Answer 3

how to find the domain and point of inflection

Answer 4

domain is everywhere except 2,-2
For inflection point and extrema you will need to take derivative of the function

Answer 5

Do you know how to take derivative?

Answer 6

yes then after taking derivative what shall i do

Answer 7

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

Answer 8

derivative is ((x^2-4)(2x)-(x^2+1)(2x))/(x^2-4)^2

Answer 9

so i equated it to zero..

Answer 10

from which i get x=0

Answer 11

then what shall I do?

Answer 12

Then the extrema is at x=0

Answer 13

you can find the inflection point

Answer 14

it says to find local extrema is that the local extrema value.

Answer 15

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.

Answer 16

time traveler?