To draw the graph using a calculator, we first press Y= and type the function in one of the available rows. Having written the function, we can push the GRAPH button to see an image of it.
For this function, we are unable to see the entire image because it does not fit in the standard viewing window. Let's resize the window by pushing WINDOW and changing the minimum and maximum of our axes. We want all of the relative minimums, maximums, and zeros to be clearly shown.
Relative Maximum and Minimum
This function has two extremes: one relative minimum and one relative maximum. To find the maximum, push 2nd, TRACE, and then choose the fourth option, maximum. Next, we need to choose a left bound and right bound for the maximum value. Finally, the calculator will ask for a guess of where the maximum might be.
We can do the same thing for the relative minimum. This time, however, we have to choose the third option, minimum.
The relative maximum is at (- 0.8441,9.3023), and the relative minimum is at (0.7108,- 0.0964).
Zeros
To find the zeros, we need to find the points at which the graph intersects the x-axis. This happens three times with this polynomial, so there are three zeros. To find a zero using the calculator, push 2nd, then TRACE, and choose the second option, zero. Once again, we need to choose bounds and make a guess for each zero.
The zeros are (- 1.6180,0), (0.6180,0) and (0.8,0).
