MATH QUESTION

Use calculus to graph the function f(x)=  X^2-2X+6/X-3

1.     

Find the domain of the function f(x).

2.      Find the fist derivertive and the second derivertive. 

3.      Use the increasing decreasing test to identify intervals on which f(x) is increasing or decreasing.

4.      Use either first derivative test or second derivative test to identify local maximum values and local minimum values.

5.      Use the test for concavity to determine intervals where the function concave up / down. Identify any inflections point.

6.      Graph the function using information from the above information.

Hint:

v  find the x and y intercepts as an additional points to plot on the graph.

v  Use calculus to find horizontal asymptote or vertical asymptote if needed. See chapter 2.