Sketching f(x) from the graph of f'(x)

J

JSmith

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Explain how you can use the graph of y = f'(x) to sketch a possible graph of the original function, y = f(x). You do not need to include a graph of y = f(x).
a4q1.jpg



So far I have: Since f'(x) goes from negative to positive at x=0, there must be a minimum on f(x) at x=0. We also know that f(x) is decreasing when x<0, because f'(x) is negative when x<0. f(x) is increasing when x>0, because f'(x) is positive when x>0.


Also, I know there is a cusp of some form at x=-1 and x=1, however I'm not sure what it would look like exactly (other than the slopes even out as you move away from the minimum, decreasing/increasing at a less rapid rate). How would I explain this?
 
Last edited:
Are you given a graph from which to work, or are you discussing the topic in general? You specify "at x=0", which does not appear to be part of the exercise, so I'm wondering.

Thank you! ;)
 
stapel said:
Are you given a graph from which to work, or are you discussing the topic in general? You specify "at x=0", which does not appear to be part of the exercise, so I'm wondering.

Thank you! ;)
Click to expand...

I thought I uploaded the graph to my post... Can you not see it?
 
The graph of f is decreasing for all x< 0. It goes more and more steeply downward as x approaches -1 from the left. Between -1 and 0 it is still decreasing but not as steeply. It "levels off" at x= 0, then starts upward slowly. After goes up slowly, going up much more steeply after x= 1.
 
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