Question

We wish to sketch the graph of the function

f(x)=x^2−3x+1/ (x−1)^2

• Find all the critical numbers of ‌f and of ‌f'. There are two of them; enter their exact values, together with the value x=1 at which f is undefined, in the first column of the table below (in ascending order : ‌a<b<c).

The second column consists of several drop-down menus. Do the following:

• for each of the intervals of ‌‌R defined by these points, select the phrase that best describes the behaviour and shape of the graph of the function ‌‌f;
• for each of the critical numbers, select the phrase that best describes their nature;
• for each of ‌±∞ and x=1, select the phrase that best describes the corresponding limiting behaviour of ‌f.

x	behavior
−∞
x<a
a=
a<x<b
b=
b<x<c
c=
x>c
∞

Answer 1