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14 Cards in this Set
- Front
- Back
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Relationship between f'(x) and 'movement' of graph |
f'(x) > 0 - curve increasing f'(x) < 0 - curve decreasing f'(x) = 0 - curve stationary |
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Monotonic increasing |
Monotonic increasing
f'(x) > 0 for all x |
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Monotonic decreasing |
Monotonic decreasing
f'(x) < 0 for all x |
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Local Maximum Stationary Point |
Local Maximum Stationary Point
f'(x) = 0 and > 0 before, < 0 after
or
f'(x) = 0 and f"(x) < 0 |
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Local Minimum Stationary Point |
Local Minimum Stationary Point
f'(x) = 0 and < 0 before, > 0 after
or
f'(x) = 0 and f"(x) > 0 |
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Stationary Point of Inflexion |
Stationary Point of Inflexion
f'(x) = 0 and same sign before and after
or
f'(x) = 0 and f"(x) = 0 and changes sign |
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Second derivative and concavity |
f"(x) > 0 - concave up f"(x) < 0 - concave down f"(x) = 0 - possible point of inflexion (must change sign) |
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Sign of f'(x) and f"(x) |
f'(x) > 0 f"(x) >0 |
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Sign of f'(x) and f"(x) |
f'(x) < 0 f"(x) < 0 |
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Sign of f'(x) and f"(x) |
f'(x) > 0 f"(x) < 0 |
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Sign of f'(x) and f"(x) |
f'(x) < 0 f"(x) > 0 |
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A relative maximum/minimum is |
A relative maximum/minimum is a maximum/minimum turning point |
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For (absolute) maximum/minimum must consider ___________________________ and values at ______________________________ |
For (absolute) maximum/minimum must consider relative maximum/minimum and values at endpoints of domain |
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Maximum/minimum problems show that |
Maximum/minimum problems show that point is in fact maximum/minimum |
