AP Calculus AB, calculus terms and theorems
Terms : Hide Images
| 720712265 | 1 |  | 1 | |
| 720712266 | 0 |  | 2 | |
| 720712267 | Squeeze Theorem |  | 3 | |
| 720712268 | f is continuous at x=c if... |  | 4 | |
| 720712269 | Intermediate Value Theorem | If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k | 5 | |
| 720712270 | Global Definition of a Derivative |  | 6 | |
| 720712271 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 7 |
| 720712272 | nx^(n-1) |  | 8 | |
| 720712273 | 1 |  | 9 | |
| 720712274 | cf'(x) |  | 10 | |
| 720712275 | f'(x)+g'(x) |  | 11 | |
| 720712276 | f'(x)-g'(x) |  | 12 | |
| 720712277 | uvw'+uv'w+u'vw |  | 13 | |
| 720712278 | cos(x) |  | 14 | |
| 720712279 | -sin(x) |  | 15 | |
| 720712280 | sec²(x) |  | 16 | |
| 720712281 | -csc²(x) |  | 17 | |
| 720712282 | sec(x)tan(x) |  | 18 | |
| 720712283 | dy/dx |  | 19 | |
| 720712284 | f'(g(x))g'(x) |  | 20 | |
| 720712285 | Extreme Value Theorem | If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval. | 21 | |
| 720712286 | Critical Number | If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined) | 22 | |
| 720712287 | Mean Value Theorem | The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line. |  | 23 |
| 720712288 | First Derivative Test for local extrema |  | 24 | |
| 720712289 | Point of inflection at x=k |  | 25 | |
| 720712290 | Combo Test for local extrema | If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c. If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c. |  | 26 |
| 720712291 | Horizontal Asymptote |  | 27 | |
| 720712292 | L'Hopital's Rule |  | 28 | |
| 720712293 | Squaring function | D: (-∞,+∞) R: (o,+∞) |  | 29 |
| 720712294 | Cubing function | D: (-∞,+∞) R: (-∞,+∞) |  | 30 |
| 720712295 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 31 |
| 720712296 | Square root function | D: (0,+∞) R: (0,+∞) |  | 32 |
| 720712297 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  | 33 |
| 720712298 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 34 |
| 720712299 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 35 |
| 720712300 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 36 |
| 720712301 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 37 |
| 720712302 | Greatest integer function | D: (-∞,+∞) R: (-∞,+∞) |  | 38 |
| 720712303 | Given f(x): Is f continuous @ C Is f' continuous @ C | Yes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp |  | 39 |
| 720712304 | Given f'(x): Is f continuous @ c? Is there an inflection point on f @ C? | This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
Yes f' decreases on X | | 40 |
