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| 6710989520 | Intermediate Value Theorem | If f(x) is continuous, there must be at least one "c" on (a,b) such that f(c) is between f(a) and f(b). | 0 | |
| 6711001789 | Extreme Value Theorem | If f(x) is continuous on [a,b] then there exists an absolute maximum and minimum on [a,b] either at critical points or endpoints. | 1 | |
| 6711009873 | Mean Value Theorem | If f(x) is differentiable then there is at least one "c" on (a,b) such that f'(c)= (f(b) - f(a))/(b-a) | 2 | |
| 6711099251 | Average Value of f(x) on [a,b] | 1/(b-a) times the Definite Integral of f(x) from a to b | 3 | |
| 6711103633 | Average Rate of change of f(x) from a to b | (f(b) - f(a))/(b-a) | 4 | |
| 6711108786 | Particle moves left | Velocity is negative | 5 | |
| 6711110370 | Object is at rest | Velocity is zero | 6 | |
| 6711111279 | Object is speeding up | velocity and acceleration have the same sign | 7 | |
| 6711115552 | Displacement | Definite integral of velocity = s(b) - s(a) | 8 | |
| 6711119045 | Total Distance | Definite integral of the absolute value of velocity | 9 | |
| 6711121334 | d/dx[c] | 0 | 10 | |
| 6711121882 | d/dx[x] | 1 | 11 | |
| 6711122965 | d/dx[x^n] | nx^(n-1) | 12 | |
| 6711125073 | d/dx[sinx] | cosx | 13 | |
| 6711125782 | d/dx[cosx] | -sinx | 14 | |
| 6711127665 | d/dx[tanx] | sec^2(x) | 15 | |
| 6711130608 | d/dx[secx] | secxtanx | 16 | |
| 6711132069 | d/dx[e^u] | u' e^u | 17 | |
| 6711133078 | d/dx[lnu] | u'/u | 18 | |
| 6711136149 | d/dx[f(x)+g(x)] | f'(x) + g'(x) | 19 | |
| 6711137765 | d/dx[f(x)g(x)] | f(x)g'(x) + g(x)f'(x) | 20 | |
| 6711139446 | d/dx[f(x)/g(x)] | [g(x)f'(x) - f(x)g'(x)]/[g(x)]^2 | 21 | |
| 6711142640 | d/dx[cf(x)] | cf'(x) | 22 | |
| 6711146863 | Definition of the derivative of f(x) | lim as h approaches zero of [f(x+h)-f(x)]/h | 23 | |
| 6711157328 | d/dx[f(g(x))] | f'(g(x))g'(x) | 24 | |
| 6711159755 | d/dx[f(g(h(x)))] | f'(g(h(x))g'(h(x))h'(x) | 25 | |
| 6711167127 | g'(x) if f(x) and g(x) are inverses | 1/(f'(g(x)) | 26 | |
| 6711174606 | f(x) is increasing | f'(x) is positive | 27 | |
| 6711175063 | f(x) is decreasing | f'(x) is negative | 28 | |
| 6711176047 | f(x) is concave up | f''(x) is positive | 29 | |
| 6711176778 | f(x) is concave down | f''(x) is negative | 30 | |
| 6711180473 | f(x) has a point of inflection at x=a | f''(a) = 0 or is undefined and there is a sign change of f''(a) at x=a | 31 | |
| 6711184030 | f(x) has a relative (local) minimum at x=a | f'(a)=0 or is undefined. Also f'(x) changes from negative to positive at x=a | 32 | |
| 6711186578 | f(x) has a relative (local) maximum at x=a | f'(a)=0 or is undefined. Also f'(x) changes from positive to negative at x=a | 33 | |
| 6711194029 | L'Hopital Rule | If the limit as x approaches h of f(x)/g(x) is an indeterminant form then it also equals the limit as x approaches h of f'(x)/g'(x) | 34 |
