Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Calculus Rules

### Rules Learned in Calc I

Fill in blank | |
---|---|

If f is ____ on the closed interval [a,b], then f attains ___ and ___ in [a,b] | continuous, absolute max, absolute min |

f(x) has an inflection point at x=c if ___. | f changes concavity at c. |

f(x) has a critical point at x=c, if ___ or ___. | f'(c)=0 or DNE |

If f'(x) is greater than 0 on Interval I, then f is ___. | increasing on I |

If f'(x) is less than 0 on interval I, then f is ___. | decreasing on I |

If f''(x) is less than 0 on Interval I, then f'(x) is ___ and f is ___. | decreasing, concave down |

If f''(x) is greater than 0 on Interval I, then f'(x) is ___ and f is ___. | increasing, concave up |

x=c is an inflection point if ___. | the concavity changes |

f(c) is an absolute max on I if ___. | f(c) is greater than f(x) for all values x in I. |

f(c) is an absolute min on I if ___. | f(c) is less then f(x) for all values x in I. |

f(c) is a local max if ___. | f(c) is greater than f(x) for all x near c. |

f(c) is a local min if ___. | f(c) is less than f(x) for all x near c. |

Assume that c is a critical point of f and that f is continuous at x=c. 1. If f'(x) changes from positive to negative, then c is ___. 2. If f'(x) changes from negative to positive, then c is ___. 3. If f'(x) does not change sign, then c is ___. | 1. Local max 2. Local min 3. Neither local max nor local min |

Assume f'' is continuous near c. 1. If f''(c) is greater than 0, then f(c) is ___. 2. If f''(c) is less than 0, then f(c) is ___. | 1. Local max 2. Local min |

If f is ___ on a closed interval (a,b), then there exists a c in (a,b), such that ___. | continuous, f'(c)=f(b)-f(a)/b-a |

If f and g are ___ and ___ near a, and the limit of f(x)/g(x) as x approaches a gives an indeterminate form of ___ or ___, then ___. | continuous, g does not equal 0, infinity/infinity. 0/0, limit as x approaches a is f'(x)/g'(x) |

A function f is continuous at a number a if ___. | The limit of f(x) as x approaches a = f(a) |

Suppose that f is ___ on the closed interval [a,b] and let N be any number between f(a) and f(b) where ___. Then there exists a number c in (a,b), such that ___. | continuous, f(a) does not equal f(b), f(c)=N |

The line x=a is a vertical asymptote when ___. | The limit of f(x) as x approaches a is infinity or negative infinity. |

Created by:
100000465038020