In Exercises 129–130, find the inflection points (if any) on the graph of the function and the coordinates of the points on the graph where the function has a local maximum or local minimum value. Then graph the function in a region large enough to show all these points simultane-ously. Add to your picture the graphs of the function’s first and second derivatives. How are the values at which these graphs intersect the x-axis related to the graph of the function? In what other ways are the graphs of the derivatives related to the graph of the function? 1
29. y = x5 - 5x4 - 240
130. y = x3 - 12x2
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To find inflection points we need second derivative.
For point of inflection y"=0 from there find x.
At x=0 , it has multiplicity 2 so it is not point of inflection.
Only point of inflection is 3
To find critical points we have to set y'=0 and sol...
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