# Calculus Test 4

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valleystudent84's
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2015-11-14 20:37

## Section

Question | Answer |
---|---|

Conditions for Rolles Theorem (3) | I = Func MUST cont on the closed interval. II= Func MUST be diff. on the open interval. III= the Y values of the end points MUST be the same |

Conditions for Mean value theorem (2) | I = Func MUST be continuous on the closed interval. II = Must be diff. on the open interval |

Extrema - Define - how to find | The extreme values in a given interval; a max or a min. Only occur at critical numbers but NOT ALL critical numbers are exterma - set second Der. to 0. Must set into original to find coordinate |

Critical numbers - define - how to find | Any Values that make the first Der. 0 or undefined - set first Der to 0 |

When the slope of the graph is 0, there is an _ | Extrema |

Critical numbers _ _ the intervals of increasing and decreasing | Break up |

1st Der Test - define - process | If the graph is increasing BEFORE a critical number and decreasing AFTER a critical number than that must be a MAX. Opposite is true for MIN - set test points into first Der. and check for sign |

Concavity - define - process | Curvature of the graph; where f"(x) is + = CU and where f"(x) is - = CD - Set f"(x) = 0 and look for PPOI. Any point where the concavity changes is a Pt of inflection. Set test points into f"(x) between these points to see the behavior |

Pts of inflection - Define | Any Pt where the concavity changes |

In concavity, where A is a pos. number = | Concave UP |

In concavity, where B is a neg. number = | Concave DOWN |

In concavity, where test Pts yield a 0, the behavior is _ | inconclusive |

In a rational equation, set _ equal to 0 to find the Asymptotes | Denominator |

In a rational equation, set _ and _ equal to 0 to find POI | Numerator - Denominator |

Horizontal and or oblique asymptotes are found how (3 ways) | Degree in N is larger than D -> No HA - Degree in D is larger -> Y=0 - degree in N and D are the same -> ratio of leading coefficients |

Three cases of lim as approaches ∞ in a rational func. | ∞ left in D = 0 - ∞ left in N = ∞ - No ∞ left = ratio of constants |

what does sin(x)/x = (in infinite limits) | 0 |

Newtons Method | X(n+1) = Xn - (Func)/(1-der) |

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