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79

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PAGE: 188SET: ExercisesPROBLEM: 79
Please look in your text book for this problem Statement

Graph the derivative function with the points:

Graph :

1. Draw the coordinate plane.

2. Plot the points.

3. Connect the points with a smooth curve.

Observe the derivative graph:

Critical points are the points where the curve touches the  - axis.

From the graph the critical points are  and .

(a)
From the first derivative test if positive on the interval , then the function increases on the interval .
The graph is decreasing on  since on .

The graph is increasing on since on .

The graph is again decreasing on since on .

Now draw the rough graph of .

(c)

Use first derivative test to identify all relative extrema.

changes from negative to positive at .

Therefore according to first derivative test , the function has minimum at .

changes from positive to negative at .

Therefore according to first derivative test , the function has maximum at .

(a)

(b) Critical points are  and .

(c) has minimum at .

      has maximum at .



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