# Thread: Need Help drawing a continuous function that satifies all conditions

1. ## Need Help drawing a continuous function that satifies all conditions

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)

2. 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!

3. Originally Posted by apcalculus
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!
How did u get that.. from (2,infinity)? And no i have it written in my note book but i dont have a scanner.

4. |x| > 2 means x < -2 or x > 2. I hope this helps.

5. Originally Posted by apcalculus
|x| > 2 means x < -2 or x > 2. I hope this helps.
Oh ok i see it now Thank you