| A | B |
|---|
| critical point | f(c) is defined and f'(c) is either zero or undefined. |
| local maximum / relative maximum | f(c) such that f(c) >= f(x) for all x in an open interval containing c. |
| local minimum / relative minimum | f(c) such that f(c) <= f(x) for all x in an open interval containing c. |
| global maximum / absolute maximum | f(c) such that f(c) >= f(x) for all x in the domain of f. A maximum can occur at an endpoint. |
| global minimum / absolute minimum | f(c) such that f(c) <= f(x) for all x in the domain of f. A minimum can occur at an endpoint. |
| concave up | The graph lies above the tangent line; f''(c) > 0. |
| concave down | The graph lies below the tangent line; f''(c) < 0. |
| concavity | The value of f''(c). |
| point of inflection / inflection point | f''(x) changes sign and f is continuous. |
| cusp | f'(c) is discontinuous. |
| plateau point | f'(c) = 0, but f'(x) does not change sign. |
| 1st Derivative Test: Local Maximum | f'(x) changes from positive to negative and f is continuous. |
| 1st Derivative Test: Local Minimum | f'(x) changes from negative to positive and f is continuous. |
| 2nd Derivative Test: Local Maximum | f'(c) = 0 and f''(c) < 0. |
| 2nd Derivative Test: Local Minimum | f'(c) = 0 and f''(c) > 0. |
| EVT: Extreme Value Theorem | If f is continuous on the closed interval [a, b], then f has a maximum and a minimum on [a, b]. |
