Question

Find the extrema of a polynomial function on a graphing calculator.

Answer 1

Extrema of a polynomial function simply represents the absolute maximum or an absolute minimum of a given polynomial function. We can also say that a polynomial function of degree $n$ has at most $n - 1$ local extrema.Now by using this basic definition we can find how to find the extrema of a polynomial function on a graphing calculator.

Complete answer:
Given statement: To find the extrema of a polynomial function on a graphing calculator.A graphing calculator is a hand held device which is capable of solving equation plotting graphs and other functions involved with variables.Now our aim is to find the extrema of a polynomial function on a graphing calculator.Some of the buttons on the graphing calculator are: ${\text{y = , 2nd, calc, and window}}$

Now the steps we should follow for finding the extrema of a polynomial function on a graphing calculator are:
1. First we have to enter the function into the button ${\text{y = }}$ since ${\text{y = }}$ button allows us to enter the function into the function bank.
2. Now we have to select the ${\text{2nd}}$ button which should be followed by the ${\text{calc}}$ button.
3. Now depending on the given question we have to select either maximum or minimum.
4. Now we have to see whether the local extrema is visible or not, if not then accordingly we have to adjust the window.
5. Now the graph is seen on the screen along with the words ${\text{'Left Bound?'}}$. Then we have to move the cursor to the left of the extrema and then hit enter such that the screen will have the words ${\text{'Right Bound?'}}$. We have to then move the cursor to the right of the extrema and then hit enter.
6. Now the screen will say ${\text{'Guess?'}}$ and then hit enter.
7. Now the screen will be showing the extrema in terms of $x\;{\text{and}}\;y$ on the bottom of the screen.

Thus following the above steps we can find the extrema of a polynomial function on a graphing calculator.

Note: ${\text{2nd}}$ Button in the calculator allows us to access the second function of the buttons. Also the ${\text{calc}}$ button is found on the top row of the calculator.After selecting this button we can choose either maximum or minimum. Also care must be taken while performing functions on the buttons since the chances of production of error is large in these types of operations.