Unformatted text preview: 8. Now do the same thing for f ‘ ’(x). This will show where the function is concave up and
concave down. When the second derivative is positive, the function is concave up, when
it is negative the function is concave down. It will also ﬁnd any inﬂection points where
the concavity changes. Find both coordinates of each inﬂection point. 9. Assuming you have done 3 and 4 above, plot all the relative max’s, min’s and infection points.
10. You should now be able to reasonably connect the dots and get a graph. If you feel you
don’t have enough points on the graph you can add a few more. Remember to correctly show where the function is increasing, decreasing, concave up and concave down.
11. Finally use the info from 2 to show behavior when |x| is large and on both sides of all discontinuities. This should be plenty of info so that you can hand sketch a reasonable graph of the function.
Here are some functions to work on: [ BE SURE to type in withmealDomain) into Maple. This will guarantee the roots will work correctly. ] YOU CAN GRAPH TO FUNCTIONS TN
MAPLE TO MAKE SURE YOUR ANALYSIS OF THE GRAPH IS CORRECT. l. f(x)=8x3—21x2+18x+2 2. f(x) = if
x —l x2
3. f(x) = m
4. f (x) = 33%;: since the ﬁmction is periodic, you can ﬁgure out the graph on the interval [0, 2Pi] and then just keep repeating the pattern. x3 5. f(X) : )62 +1 ...
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- Fall '10