Behaviors of F(x), F'(x), & F''(x)
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13 Terms
When f(x) is increasing, what do we know about f’(x)?
It is positive
When f(x) is decreasing, what do we know about f’(x)?
It is negative
When f(x) has a horizontal tangent, what do we know about f’(x)?
f’(x) = 0
When f(x) = 0 what do we know about f’(x)?
It has a horizontal tangent
When f(x) has a local max, what do we know about f’(x)?
f’(x) = 0 or is undefined
When f(x) has a local min, what do we know about f’(x)?
f’(x) = 0 or is undefined
When f’(x) has a local max, what do we know about f(x)?
f(x) = 0 or is undefined
When f’(x) has a local min, what do we know about f(x)?
f(x) = 0 or is undefined
when f(x) has a local max, how does f’(x) respond?
f’(x) > 0 to the left & f’(x) < 0 tot he right
when f(x) is concave up what is the behavior of f’(x)?
f’(x) is increasing
when f(x) is concave down what is the behavior of f’(x)?
f’(x) is decreasing
when f(x) is concave up and f’(x) is increasing, what is the behavior of f’’(x) ?
f’’(x) is positive
when f(x) is concave down and f’(x) is decreasing, what is the behavior of f’’(x) ?
f’’(x) is negative