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# sketching a curve of cubic function having min and max points

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1. Hi guys,
I'm trying to sketch a graph of cubic function on the attachment hence find out where the function is increasing . My problem is I'm not sure about how the graph will actually look like(i've sketched it already but it dosent seem right considering the min and max points), any help would be much appreciated
Attached Images

2. (Original post by Alen.m)
Hi guys,
I'm trying to sketch a graph of cubic function on the attachment hence find out where the function is increasing . My problem is I'm not sure about how the graph will actually look like(i've sketched it already but it dosent seem right considering the min and max points), any help would be much appreciated
Those aren't the minimums and maximums, they are the roots of the cubic. i.e: where they cut the x-axis. So you should draw a cubic starting the bottom left and moving upwards, cutting the x-axis at -6, continuing, hitting a maximum and then coming back down the cut the x-axis at x=-3 and then continuing before hitting a minimum and moving back upwards to cut the x-axis at x=2 and then moving upwards indefinitely. So your graph seems fine? What's the specific question that you have?
3. (Original post by Zacken)
Those aren't the minimums and maximums, they are the roots of the cubic. i.e: where they cut the x-axis. So you should draw a cubic starting the bottom left and moving upwards, cutting the x-axis at -6, continuing, hitting a maximum and then coming back down the cut the x-axis at x=-3 and then continuing before hitting a minimum and moving back upwards to cut the x-axis at x=2 and then moving upwards indefinitely. So your graph seems fine? What's the specific question that you have?
But the point (-6 , -30) dosent show the min part of the graph, neither the (-3 , -25 ) which should be the max part of the graph
4. (Original post by Alen.m)
But the point (-6 , -30) dosent show
What? We know that x=-6 means y=0. i.e: (-6, -30) isn't a valid point. What's the original question?
5. Not sure what you have done here - your graph is correct however your turning points are not. You should get a minimum at x=0 and a maximum at x= -14/3
6. (Original post by PhysicsIP2016)
Not sure what you have done here - your graph is correct however your turning points are not. You should get a minimum at x=0 and a maximum at x= -14/3
Here's the full question and answer to it both. In last Part of the question im fine using nature of turning points to answer that but i wanted to know what the graph looks like so i can answer it from there which is easier for me. Considering nature of turning points at their coordinates, my graph wouldnt be correct 😔Attachment 536663536665
Attached Images

7. (Original post by Zacken)
What? We know that x=-6 means y=0. i.e: (-6, -30) isn't a valid point. What's the original question?
Here's the full question and answer to it both. In last Part of the question im fine using nature of turning points to answer that but i wanted to know what the graph looks like so i can answer it from there which is easier for me. Considering nature of turning points at their coordinates, my graph wouldnt be correct 😔Attachment 536667536669
Attached Images

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