Connecting Features of f,f',and f''
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When f'(x) is increasing, f(x) is _____________________ and f''(x) is ___________________.
concave up, positive
An x- intercept on f'(x) corresponds to a ______________ of f(x)
critical point
when f'(x) is positive, f(x) is
increasing
When f''(x) is ______ f(x) is concave down
negative
f(x) has a relative maximum when f'(x) changes from
positive to negative
Points of inflection of f(x) are ______ on the graph of f'(x)
relative extrema
When f'(x) changes signs f(x) has
relative extrema
When the ____ of f(x) are decreasing f"(x) is negative
slopes
the _____ of f'(x) give the slopes of f(x)
y-values
