I was given f''(x) and f'(x), along with the following table and the restriction that the limit as x approaches infinity of f(x)=0 (which I know means there is an asyumptote somewhere but I'm not sure where)
x 0 2 3 4 5 6
f(x) -25 -100 -200 -75 0 -10
I'm also given a chart that list's f''(x) as negative from negative infinity to (not defined, 3) then its negative again from (3, 5) or (not defined, 0) and then from (0,5) on its negative again. This would mean the graph is always concave down right?
f'(x) is negative from negative infinity to (not defined, 3) then postive from (3,5) or (not defined,0) and then negative again from (0,5) to infinity. This means the graph would be decreasing, increasing, then decreasing again correct?
I have to find the intervals where "f" is concave down? Would that be all of them? I also have to find the equation of each vertical tagent line. I think that has something to do with the limit as x approaches infinity but I'm not sure how to do that. Finally, I have to find the points of inflection. Do I let x equal zero in the equation found to get the points of inflection? THANKS!
x 0 2 3 4 5 6
f(x) -25 -100 -200 -75 0 -10
I'm also given a chart that list's f''(x) as negative from negative infinity to (not defined, 3) then its negative again from (3, 5) or (not defined, 0) and then from (0,5) on its negative again. This would mean the graph is always concave down right?
f'(x) is negative from negative infinity to (not defined, 3) then postive from (3,5) or (not defined,0) and then negative again from (0,5) to infinity. This means the graph would be decreasing, increasing, then decreasing again correct?
I have to find the intervals where "f" is concave down? Would that be all of them? I also have to find the equation of each vertical tagent line. I think that has something to do with the limit as x approaches infinity but I'm not sure how to do that. Finally, I have to find the points of inflection. Do I let x equal zero in the equation found to get the points of inflection? THANKS!