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# AP Calculus Unit 2

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

Derivative | instantaneous rate of change / slope of the tangent line |

when g'(x) > 0... | g(x) is increasing |

when g(x) is increasing... | g'(x) > 0 |

when g'(x) < 0... | g(x) is decreasing |

when g(x) is decreasing... | g'(x) < 0 |

when g(x) has an extrema... | g'(x) = 0 |

when g'(x) = 0... | g(x) has an extreme |

Power Rule | 1) multiply LC of term by exponent -- 2) sutbract 1 from the exponent |

Derivative Of Sine Is... | cosine |

Derivative Of Cosine Is... | -sine |

Root To Exponent | inside / outside |

Horizontal Tangent | f'(x) = 0 -- slope of tangent line is 0 |

Critical Values Give Us... | possible relative extrema |

How To Create Sign Graph | 1) find derivative of equation -- 2) set equation equal to zero to get critical values -- 3) put critical values on graph -- 4) plug in number in each interval to find pos or neg value |

Maximum Of g(x) Occurs When... | g'(x) goes from + to - |

Minimum Of g(x) Occurs When | g'(x) goes from - to + |

When Using Trig On Sign Graphs | identify where values will be positive or negative using unit circle |

Tangent Line Equation | y1-y2 = m (x1-x2) |

To Make A Tangent Line Equation, You Need... | a point & a slope |

A Double Root Indicates... | the sign does not change |

Horizontal Tangent Is The Same As Saying... | Critical Values |

Only Plug Into The Original Equation To Find... | a y value |

How To Calculate Slope | y1-y2 / x1-x2 |

Normal Line (didnâ€™t review) | line perpendicular to the tangent line at the point of tangency |