Those interpretations look good. The only thing I would add is that it is also decreasing for x values from 2 to infinity. Do you have a sketch? It shouldn't be too hard to put these pieces together.
Good luck!
I need help to see if my diagram i made at home is correct. I wrote my observations and if someone can include a diagram it would be greatly appriciated
Sketch the graph of a continuos function that satisfies all of the following conditions:
f'(x)>0 if /x/ <2 {/x/= absolute value of x}
f'(x)<0 if /x/ >2
f'(2)=0
lim as x approaches positive infinity f(x)=2
f(-x)=-f(x)
f''(x) if 0<x<3
f''(x)>0 if x>3
soo i got the following
- increasing from (-2,2)
-decreasing from (-infinity,-2)
-hoizontal tanget at x=2
-vertical asyp at x=2
-odd function
-concave down from (0,3)
-concave up from(3, infinity)