TRIGONOMETRIC FUNCTIONS Graphing And Analysis (Page 9 of 13)

Now we will find the absolute minimum using the CALC minimum command. However, this time we will answer the three questions by entering values of x directly without relying on the arrow keys. Just type in the value of x you want, and a prompt will appear as you do. Based upon our results for the two x-intercepts, we will use a left bound of 1.8, a right bound of 2.1, and a guess of 1.95. As you can see, the absolute minimum occurs at approximately (1.96, -1).

 2nd CALC key. 3: menu selection. 1.8 ENTER key. 2.1 ENTER key. 1.95 ENTER key. Calculator screen image.

The range of this function is [-1, 5]. The function is increasing on [π/4, 1.18)union(1.96, 3π/4] and decreasing on (1.18, 1.96], approximately.

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