Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. y=x^{3}-3x^{2},[-2,5] by [-10,10]

Chaya Galloway 2021-02-20 Answered
Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. y=x33x2,[2,5]by[10,10]
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Answered 2021-02-21 Author has 108 answers

Step 1
y=x33x2,[2,5]×[10,10]
The graph of this function in the indicated viewing window is shown in the following picture.
image


Step 2
As we can see in this picture this function has:
A local maximum that occurs at the point (0, 0).
A local minimum that occurs at the point (2,-4).
For the domain:
This is a polynomial function so it is defined for all values of x in the set of real numbers.
The domain is: D=(,+)
For the range:
This function can get all values in the set of real numbers (vertical axis) so:
The range is: R=(,+)

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