the critical number would be the -2/3? i plug that into the original equation and obtain the y-value?
You have a positive sign on both sides of the critical value, and since the second derivative is a linear function with positive slope, we know it must go from negative to positive across the critical value. You found the correct value, I just wanted you to be aware of the change of sign of the second derivative. In fact, if the sign does not change, then you do not have a point of inflection.
If you are asked for the inflection point, then you need the y-value, so plug the critical number into the oriinal function to get the y-coordinate of the inflection point. What does the sign of the second derivative on either side of the critical value tell you about concavity?
ok this is what i got...
https://www.dropbox.com/s/y9fckjmulj...2012.03.32.jpg
this is my inflection point, right?
what do i do next??
Let's review what you need to do:
a) find where f(x) is increasing/decreasing
b) where it is concave up/concave down
c) local max/min
d) and then finally sketch the curve of the graph
a) You have done this, but can you formally give the intervals where the function is increasing/decreasing?
b) you have the information to answer this, can you state it?
c) you have the information to answer this, and two ways to identify the nature of the extrema...can you show this? Can you give the points and state whether they are maxima or minima?
d) I would also find the intercepts, then along with the previous steps, you have enough information to accurately sketch the graph.
how about this? https://www.dropbox.com/s/140k0ylovc...2015.44.18.jpg
https://www.dropbox.com/s/i993jzz8e3...2016.08.11.jpg
why is this so hard???