Concavity and Extrema

Front

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

Back

an inflection point

Front

What will be true at an inflection point? (select the best answer)

Back

f''(x)=0

Front

The concavity of a function is described by its _______________.

Back

second derivative

Front

The slope of a function is described by its _____________.

Back

first derivative

Front

Derivative means the same thing as _____________.

Back

slope of the tangent line

Front

If f''(x) > 0, the function is _____________.

Back

concave up

Front

If f''(x) < 0, the function is _____________.

Back

concave down

Front

A point where the first derivative f'(x) changes from positive to negative is a _____________.

Back

relative maximum

Front

A point where the first derivative f'(x) changes from negative to positive is a _____________.

Back

relative minimum

Front

The second derivative test can be used to determine _____________.

Back

the nature of critical points