CalcAB Quiz 5.1 - 5.3B Need to Know

Critical Numbers

Values of x where the derivative is zero or undefined, indicating potential local maxima or minima.

Inflection Point

A point on the graph where the concavity changes; determined when the second derivative is zero or undefined.

Concave Up

When the second derivative is positive, indicating the graph is curving upwards.

Concave Down

When the second derivative is negative, indicating the graph is curving downwards.

Increasing Interval

An interval where the first derivative is greater than zero, indicating the function is rising.

Decreasing Interval

An interval where the first derivative is less than zero, indicating the function is falling.

Local Maximum

A point where the function reaches a value higher than its neighboring values.

Local Minimum

A point where the function reaches a value lower than its neighboring values.

Rolle’s Theorem

If a function is continuous on a closed interval and differentiable on the open interval, and the function has equal values at the endpoints, then there exists at least one c in the open interval such that f'(c) = 0.

Mean Value Theorem

If a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one c in the open interval where f'(c) equals the average rate of change of the function on that interval.

Extrema

The maximum and minimum values of a function on a given interval.

First Derivative Test

A method to determine local maxima and minima by analyzing the sign of the first derivative.

Second Derivative Test

A method to determine the concavity of a function and identify local extrema using the second derivative.