Draw graph given f'(x), f''(x), domain, etc. Please check?

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The discussion revolves around sketching a graph based on given derivatives and domain information. Key concerns include accurately representing concavity and convexity within specified intervals, as well as handling points where the second derivative is zero. The user seeks clarification on whether the graph should reflect complete concavity or just the beginning of it. Additionally, there is uncertainty about the angle of the graph near a point where no limit exists. Overall, the focus is on ensuring the graph accurately depicts the behavior of the function based on its derivatives.
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1. I was asked to roughly sketch a graph given the information seen, in the below picture, to the right of the graph.

28rcitw.jpg


2. My actual graph is done by hand and the lines are not as straight, but the general shape is the same.

Does it look approximately right?

The areas I am worried about are:
a) when it specifies being concave of convex between certain intervals: whether it means completely visible between those intervals as concave/convex or just beginning to appear concave/convex

b) where it says "no limit of y x -> -2" exists, whether or not I should have drawn it the same angle as I did, or started the one to the left of -2 from a different angle.
 
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First, label the axis, and adopt the dot convention where a solid dot contains that point and a circle indicates a hole. Everything looks okay until you get to the second derivitive/concavity. The points where the second derivative would be zero (in between the domain of concavity given) should be points, and after that it should have a curve. For instance, when it says that from 5 to 10 (for example) f'' is positive, that means the graph should "open upwards" from 5 to 10, and if f'' is negative from 10 to infinity, then it should curve back downwards.
 
Thanks, QuarkCharmer.

To you or anyone who sees, I'm just wondering if this one is more accurate? Again, aside from the straight line, which I know means f"(x) = 0.

2cd9hz.jpg
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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