# Calc Final Exam Review chp2

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2015-12-09 17:45

## Section

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

T or F? If a function h is continuous at a point x = a, then h must be differentiable at point at x=a | False, there can be a corner or a cusp. |

When can a limit fail to exist? | A limit can fail to exist if 1) the right and left limits are not the same, 2) if the function goes to + or - infinity |

What is a vertical asymptote? | It means that as x->a, f(x)->∞ cannot be touched by function |

What is a horizontal asymptote? | It is a horizontal line that shows the behavior far off of the graph, can be touched |

f is differentiable at a if | f'(a) exists |

Relationship between differentiability and continuity | If f is differentiable, then f is continuous. f may not be differentiable if f is continuous |

When is a function not differentiable? | If there is a corner or cusp, jump or removable discontinuity, or if there is a vertical tangent |

What does f' say about f? | If f' is positive, f is inc/ if f' is negative, f is dec. If f'=0, then that is an inflection point for f |

What does f'' say about f? | If f'' is positive, f is concave up, if f'' is negative, f is concave down |

What happens at an inflection point? | The concavity of f changes |

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