Question

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]

Polynomial graphs
ANSWERED
asked 2021-02-20
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. \(\displaystyle{y}={x}^{{{3}}}-{3}{x}^{{{2}}},{\left[-{2},{5}\right]}{b}{y}{\left[-{10},{10}\right]}\)

Answers (1)

2021-02-21
Step 1
\(\displaystyle{y}={x}^{{{3}}}-{3}{x}^{{{2}}},{\left[-{2},{5}\right]}\times{\left[-{10},{10}\right]}\)
The graph of this function in the indicated viewing window is shown in the following picture.
\(\displaystyle{h}{\mathtt{{p}}}{s}:{/}{q}{2}{a}.{s}{3}-{u}{s}-{w}{e}{s}{t}-{1}.{a}{m}{a}{z}{o}{n}{a}{w}{s}.{c}{o}\frac{{m}}{{d}}{e}\frac{{v}}{{19610300971}}.{j}{p}{g}\)
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: \(\displaystyle{D}={\left(-\infty,+\infty\right)}\)
For the range:
This function can get all values in the set of real numbers (vertical axis) so:
The range is: \(\displaystyle{R}={\left(-\infty,+\infty\right)}\)
0
 
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