Question 1209503
.
The function satisfies the following:
Find the rule of the fractional function that satisfies the following:

1. Its domain is ℝ / {2, -3}.


2. It has critical points at x = -2 and x = 1.


3. It has a local minimum at (-2, 1) and a local maximum at (1, 3). It is increasing on the interval ]-∞, -3[ ∪ [-2, 1] and decreasing on the remaining intervals of the domain.


4. It is concave upward on the interval ]-∞, -1] / {-3} ∪ ]2, +∞[.


5. It is concave downward on the interval [-1, 2[.


6. It has an inflection point at (-1, 2).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



To check the solution by @PChill in his post,  I plotted the graph of the function   f(x) = {{{(x^2+x-2)/((x-2)*(x+3))}}},

using free of charge online plotting tool  DESMOS


www.desmos.com/calculator


( see the plot under this link https://www.desmos.com/calculator/owlvob9k0d )



The plot shows that this function


      - does not satisfy condition  (2);

      - does not satisfy condition  (3);

      - does not satisfy first of the two conditions  (4);

      - does not satisfy condition  (5).



<U>CONCLUSION</U>: &nbsp;&nbsp;the solution by &nbsp;@PChill to this problem is &nbsp;INCORRECT.