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Increasing and Decreasing Functions Problems

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2. (2--6) Determine the intervals on which the function is decreasing and increasing and then find local minima and maxima.
3.
4.
5.
6. The graph of is located below the X-axis but it touches the -axis at . What can you say about the graph of ?

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Increasing and decreasing functions are investigated. The solution is detailed and well presented.

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2. (2--6) Determine the intervals on which the function is decreasing and increasing and then find local minima and maxima.
= x2 + x - 6
f'(x) = 2x + 1 = 0  x = -½ is a critical point.
At x = 0, f'(x) = 1 >0
At x = -1, f'(x) = -2 + 1 = -1 < 0
Therefore, f(x) is decreasing in the interval and increasing in the interval ...

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