1. ## Re: sketching curve graph

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?

2. ## Re: sketching curve graph

the critical number would be the -2/3? i plug that into the original equation and obtain the y-value?

3. ## Re: sketching curve graph

Yes, this will give you the point on the curve where concavity changes.

4. ## Re: sketching curve graph

ah, i see. ok i will continue this problem in the morning, thank u for ur help, will probably need more of it in the morn.

5. ## Re: sketching curve graph

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??

6. ## Re: sketching curve graph

Yes, your inflection point is $\displaystyle \left(-\frac{2}{3},-\frac{20}{27} \right)$.

Now, what can you say about concavity?

7. ## Re: sketching curve graph

Originally Posted by Prove It

- Hollywood

8. ## Re: sketching curve graph

now i plot the points on a number line and determine the trend before after and in between??

9. ## Re: sketching curve graph

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.

10. ## Re: sketching curve graph

how do i find the intercepts? im sorry if its obvious, but im just finding all of this so very confusing right now.

12. ## Re: sketching curve graph

To find the x-intercepts, set f(x) = 0 and solve for x. You should find 3 roots, and this function factors nicely.

To find the y-intercept, let x = 0, and so it will be (0,f(0)).

What do you find?

13. ## Re: sketching curve graph

im doing this to the original function or to f"?

14. ## Re: sketching curve graph

To the original function, as this is the curve you are being asked to sketch.

15. ## Re: sketching curve graph

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