Unit 5: Analytical Applications of Differentiation (copy)

Mean Value Theorem (MVT)

Links the average rate of change and the instantaneous rate of change.

Extreme Value Theorem

States that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval.

Extrema

Maximum and minimum values of a function, which can be absolute (global) or local (relative).

Critical Points

Points where a function's derivative is zero or undefined, indicating potential extrema.

Increasing Function

A function where f’(x) > 0.

Decreasing Function

A function where f’(x) < 0.

Relative Extremum

A point where the function has a local maximum or minimum, determined by changes in the first derivative.

Candidate’s Test

A method for finding absolute extrema by considering critical points and endpoints.

Concavity

The property of a function indicating whether it is curving up (concave up) or down (concave down) based on the sign of the second derivative.