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? 129. y = x5 - 5x4 - 240130. y = x3 - 12x2

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Asked Jan 17, 2020
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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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Expert Answer

Step 1

Since you have submitted two questions, we'll answer the first question. For the second question please submit the question again and specify it.

To find inflection points we need second derivative.

Calculus homework question answer, step 1, image 1
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Step 2

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

Calculus homework question answer, step 2, image 1
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Step 3

To find critical points we have to set y'=0 and sol...

Calculus homework question answer, step 3, image 1
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