F'(x) graph behavior

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10 Terms

1
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f'(x) is positive(above x-axis)

f(x) is increasing

2
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f'(x) is negative (below x-axis)

f(x) is decreasing

3
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f'(x) changes from negative to positive ( from below to above x-axis)

f(x) has local min

4
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f'(x) changes from negative to positive

From below to above x-axis

5
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f'(x) changes from positive to negative (from above to below x-axis)

f(x) has local max

6
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f'(x) changes from positive to negative

From above to below x-axis

7
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f'(x) is increasing (positive slope)

f(x) is concave up

8
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f'(x) is decreasing (negative slope x)

f(x) is concave down

9
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f'(x) change from decreasing to increasing

point of inflection

10
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f'(x) change from increasing to decreasing

point of inflection