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


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