Calc AB Unit 4-5 Test Review Vocab & Justifications

Front

If f '(3) = 0 and f "(3) > 0, what can be concluded about f(x)?

Back

There is a local minimum at x = 3.

Front

If f'(x) > 0 over an interval, what does this indicate about f(x)?

Back

f(x) is increasing over that interval.

Front

What condition indicates that a particle is at rest?

Back

v(t) = 0.

Front

What does v(t) > 0 signify about a particle's motion?

Back

The particle is moving to the right.

Front

What does it mean when f'(x) changes from positive to negative?

Back

There is a relative maximum.

Front

Define a local maximum.

Back

A point where the function value is higher than all nearby points.

Front

Define a local minimum.

Back

A point where the function value is lower than all nearby points.

Front

What is the significance of f''(x) > 0?

Back

The function is concave up at that point.

Front

What does f''(x) < 0 indicate?

Back

The function is concave down at that point.

Front

What is the relationship between the first derivative and increasing functions?

Back

If f'(x) > 0, then f(x) is increasing.