Connecting 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 ___ to ___
positive, negative
Points of inflection on f(x) are ___ on the graph of f'(x)
relative extrema
When the 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 f(x)
y-values
