Calculus: Local Extrema and Derivative Tests

These flashcards cover concepts related to local extrema, critical points, and derivative tests in calculus.

What is the First Derivative Test used for?

To determine if a critical point is a local maximum or minimum in a continuous function.

What condition indicates a local minimum using the First Derivative Test?

If f' changes from negative to positive at a critical point.

What does a critical point represent in calculus?

A point where f'(p) = 0 or f'(p) is undefined.

What indicates a local maximum using the First Derivative Test?

If f' changes from positive to negative at a critical point.

What is the Second Derivative Test used for?

To determine the nature of a critical point in terms of local minima and maxima.

What does it mean if f''(p) is greater than 0?

The function has a local minimum at the critical point p.

What is indicated if f''(p) is less than 0?

The function has a local maximum at the critical point p.

What should be concluded if f''(p) equals 0?

The Second Derivative Test is inconclusive.

What is a local maximum?

A point where a function reaches a high value compared to points in its immediate vicinity.

What is a local minimum?

A point where a function reaches a low value compared to points in its immediate vicinity.

What is the definition of local extrema?

Points that are local maxima or minima within a certain interval.

In the context of local extrema, what do critical points refer to?

Locations where the derivative equals zero or is undefined, indicating potential minima or maxima.