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 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. $$\displaystyle{y}={x}^{{{3}}}-{3}{x}^{{{2}}},{\left[-{2},{5}\right]}{b}{y}{\left[-{10},{10}\right]}$$ 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: $$\displaystyle{R}={\left(-\infty,+\infty\right)}$$