Thread: local min/max and critical points

1. local min/max and critical points

Indicate on the graph of the derivative function in the figure below the -values that are critical points of the function itself. At which critical points does have local maxima, local minima or neither?

here is the image they provide

So I'm not really sure what is going on here. It looks to me that -2, -1, and 0 are critical points. I'm not sure what is the min and max though. I would think that -1 is a max and the local mins are located around -1.7 and -.3 or so, but that isn't an option. Can anyone tell me where the critical points actually are, and where the local min/max are?

2. Originally Posted by billabong7329
Indicate on the graph of the derivative function in the figure below the -values that are critical points of the function itself. At which critical points does have local maxima, local minima or neither?

here is the image they provide

So I'm not really sure what is going on here. It looks to me that -2, -1, and 0 are critical points. I'm not sure what is the min and max though. I would think that -1 is a max and the local mins are located around -1.7 and -.3 or so, but that isn't an option. Can anyone tell me where the critical points actually are, and where the local min/max are?
Hint1: Critical points occur when f ' (x) = 0 (and when it is undefined)

Hint 2: when f ' (x) > 0, f(x) is increasing, when f ' (x) < 0, f(x) is decreasing. We have a max at a point if we are increasing on the left and decreasing on the right of that point. Similar for min

3. Originally Posted by billabong7329
Indicate on the graph of the derivative function in the figure below the -values that are critical points of the function itself. At which critical points does have local maxima, local minima or neither?

here is the image they provide

So I'm not really sure what is going on here. It looks to me that -2, -1, and 0 are critical points. I'm not sure what is the min and max though. I would think that -1 is a max and the local mins are located around -1.7 and -.3 or so, but that isn't an option. Can anyone tell me where the critical points actually are, and where the local min/max are?
Ok based on your picture there are relative maxes at $x=-1$...and there are relative minimums at $x=-1.7,x=-.3$ but you cant be exact without the equation...the critical points are all three of those points...I can't see the attached website...so that is the best I can do

4. Originally Posted by Mathstud28
Ok based on your picture there are relative maxes at $x=-1$...and there are relative minimums at $x=-1.7,x=-.3$ but you cant be exact without the equation...the critical points are all three of those points...I can't see the attached website...so that is the best I can do
you do realize that this is a graph of f ' (x) not f(x)

5. Thanks for the help, I ended up figuring it out and getting it right =)

I have another that is confusing me

Consider the function f(x) = xln(x) , x > 0

Find the critical point of
Find the local maximum of f

find the local minimum of f

then I have to put the intervals on which f is increasing as well as the intervals on which f is decreasing.

So, in order to find the critical points, I have to take the derivative of the function right? thats what I did.

I ended up with f '(x) = 1 + lnx so I plugged that in and my critical point was .3678, not sure if that is right.

I don't see any local max or min, so I'm not sure. It looks like the graph is constantly decreasing, so I'm really not sure what to do with this. Can I get a hint maybe?

6. Originally Posted by billabong7329
Thanks for the help, I ended up figuring it out and getting it right =)

I have another that is confusing me

Consider the function f(x) = xln(x) , x > 0

Find the critical point of
Find the local maximum of f

find the local minimum of f

then I have to put the intervals on which f is increasing as well as the intervals on which f is decreasing.

So, in order to find the critical points, I have to take the derivative of the function right? thats what I did.

I ended up with f '(x) = 1 + lnx so I plugged that in and my critical point was .3678, not sure if that is right.

I don't see any local max or min, so I'm not sure. It looks like the graph is constantly decreasing, so I'm really not sure what to do with this. Can I get a hint maybe?
Use the fact that if $f'(a)=0$ then if $f''(a)<0$ then $a$ is a max and if $f''(a)>0$ $a$ is a min