Unit 5: Derivatives, Concavity, Extremas, Increasing/Decreasing, Points of Inflection Need to Knows
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28 Terms
If f(x) is concave up, f’(x) is…
Increasing
If f(x) is concave up, f“(x) is…
>0 (Positive)
If f(x) is concave down, f’(x) is…
Decreasing
If f(x) is concave down, f”(x) is…
<0 (Negative)
If f(x) has a point of inflection, f’(x) has…
A maximum or a minimum
If f(x) has a point of inflection, f”(x) has…
A zero and a change of signs (+/-)
If f’(x) is increasing, f(x) is…
Concave Up
If f’(x) is increasing, f”(x) is…
>0 (Positive)
If f’(x) is decreasing, f(x) is…
Concave Down
If f’(x) is decreasing, f”(x) is
<0 (Negative)
If f’(x) has a maximum or a minimum, f(x) has…
A point of inflection
If f’(x) has a maximum or a minimum, f”(x) has…
A zero and changes signs (+/-)
If f”(x)>0, f(x) is…
Concave Up
If f”(x)>0, f’(x) is…
Increasing
If f”(x)<0, f(x) is…
Concave Down
If f”(x)<0, f’(x) is…
Decreasing
If f”(x) has a zero and changes signs, f(x) has…
A point of inflection
If f”(x) has a zero and changes signs, f’(x) has…
A maximum or a minimum
If f(x) is increasing, f’(x) is…
>0 (Positive)
If f(x) is decreasing, f’(x) is...
<0 (Negative)
If f(x) has a relative maximum, f’(x) has…
A zero and changes from positive to negative
If f(x) has a relative minimum, f’(x) has…
A zero and changes from negative to positive
If f’(x)>0, f(x) is…
Increasing
If f’(x)<0, f(x) is…
Decreasing
If f’(x) = 0 and changes from positive to negative, f(x) has…
A relative maximum
If f’(x) = 0 and changes from negative to positive, f(x) has…
A relative minimum
If f’(x) = 0 and f”(x)>0, then f has…
A relative minimum
If f’(x) = 0 and f”(x)<0, then f has…
A relative maximum