Unformatted text preview: GROUP WORK 3, SECTION 4.3
Graphing with the Derivative (Form B) This exercise is designed to illustrate how numerical information from a function and its derivatives can be
used to get a very good sense of how the function looks. While it' is a good idea to use your graphing calculator
to check your ﬁnal answers, it would be missing the point to use it earlier. Consider the function f(x)=x‘/3(x-4) I. Where are the zeros (roots) of f? 2. Does f’ have any points x where f ’ (x) = 0? Where f’ (x) is not deﬁned? 3. On what intervals is f increasing? On what intervals is it decreasing? 4. Where are the local maxima and minima of f? 5. Does f ” have any points x where f” (x) = 0? Where f” (x) is not deﬁned? 6. Where is f concave up? Where is it concave down? 7. Where are the inﬂection points of f? 8. Using this information, sketch a graph of y = f (x) on a separate piece of paper. ...
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