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`f(x)=(1)/(x^(2)-2x+2)` <br> `=(1)/((x-1)^(2)+1) gt 0, AA x in R` <br> `f(0)=1`, hence the graph intersects the y-axis at (0,1). <br> `f(x)!=0` for any real x, hence the graph never intersects the x-axis. <br> Further `x^(2)-2x+2!=0` for any real x, hence the function has no verical asymptote. <br> Also the degree of the denominator is higher than the degree of the numerator, hence the graph has horizontal tangent x = 0. <br> `f'(x)=(2x-2)/((x^(2)-2x+2)^(2))` <br> `f'(x)=0 :. x=1`, which is the point of maxima. <br> For `x in (-oo,1),f(x)` increases and for `x in (1, oo), f(x)` decreases. <br> Also `f(1)=1` <br> From the above discussion, the graph of the function is shown in the following figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C06_S01_023_S01.png" width="80%"> <br> Since `f(1-x)=f(1+x)`, the graph is symmetrical about the line x = 1.Transcript

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00:00 - 00:59 | students today's question is any to draw the graph of x is equal to 1 divided by x square - 2 X + will get effects is equal to 1 by x square - 2 x minus 2 will write one plus one so what will get one by x minus 1 whole square + 1 will observe this denominator is always more than equal to one active at x is equal to what is equal to 13 nominated in getting equal to numerator that wins at X equal to 1 upon 1 basically will get value one now denominator is always positive |

01:00 - 01:59 | and denominator more than numerator the maximum value will get one people see the graph of the graph below at x is equal to zero at x is equal to zero we are getting value 1 by 2 and x is equal to -1 x is equal to minus what we are getting at x is equal to -1 we are getting value even so this below we are getting at x is equal to zero we are getting one by two graph editor is strictly positive by this logic discriminant also it will be so will get for minor it is equal to minus 4 less than zero denominator is displacement is technique negative for the denominator is function denominator is August cost |

02:00 - 02:59 | if x approaches Infinity this function will approach to approach 20 find out app-ads.txt will be equal to x square x square - 2 X + b whole square minus minus differentiation of denominator the success permanent way bill limit to x minus 1 now what we are getting this is equal to 1 minus 1 divided by minus 2 x minus 2 is become 2 divided by x square - 2 X + square metre is positive |

03:00 - 03:59 | write two people take two common 1 - 3 x is changing its time at point is equal to 1 square - 2 X + b whole square is more than what we are getting negative that means at point x is equal to one is negative and positive on this site is changing from at less than 1 any value will take at less than what that is half negative of something might become positive slope is changing at this point point x is equal to the graph will be of the form adt-1 what is the value as one upon one but we're getting this type of 111 is one no one is now at this point we are getting |

04:00 - 04:59 | something like this type of -1 we are getting 1 + 1 + 21 + 2 + 1 by 5 and minus one will get the graph will be somewhat like this and it will look like this at approaches to infinity it will dysfunction is going to approach 20 this it like that and this is going to be at the end like this as X approaches Infinity it is getting somewhat like this one by fine now this is the turning point in this little more |

05:00 - 05:59 | x minus infinity will be like this is 150 - the final graph the final graph and this is the point of x is equal to what is the point of local Maxima or global level of the this is the Global Maxima thank you |