Thread: f(x) graph based on derivative graph help
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Old December 31st, 2008, 11:40 PM
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Originally Posted by OnMyWayToBeAMathProffesor View Post
Hello MHF,

I am stuck on part c of this question and am not 100% sure on a and b either. There is a table involved. It is attached.

Attachment 9426

a) What are the x-coordinates of all absolute maximum and absolute minimum points of f on the interval \left[-3, 3\right]. Justify your answer.

b)What are the x-coordinates of all points of inflection of f on the interval \left[-3, 3\right]? Justify your answer.

c) Sketch a graph that satisfies the given properties of f.

a-answer) i got x=1 for a maximum because the f'(x) goes from negative y values to 0 back to negative y values. is this correct?

b-answer) point of inflections occurs when f''(x)=0 and thats and x=1, I don't think there are any other points, correct?

c-answer) i could never figure out how to do that on MHF but i have seen other people do it. All my graphs don't seem to work, but from the chart i think there are 2 separate functions?

any help, especially with c would be greatly appreciated. Thanks.
something confuses me about the table. you have two possibilities for x = 1. the derivatives can be zero or undefined. which is it?

for (c), does this help?
- where the first derivative is positive, the graph is increasing. (going up as you move from left to right)
- where the first derivative is negative, the graph is decreasing. (going down as you move from left to right).
- where the first derivative is zero or undefined, you have a critical point. these can be maximums, minimums, inflection points, etc.

- where the second derivative is positive, the graph is concave up (curved like a U or a smile)
- where the second derivative is negative, the graph is concave down (curved like a \cap or a frown)
- if the second derivative is zero, you have a possible inflection point. you can test if this is the case. an inflection occurs if the second derivative changes sign on either side of the point you are concerned with


so drawing a graph based on the table means you have to follow the behavior described by these properties where appropriate
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