# Calc Final Exam Review Part Chp4

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2015-12-09 19:27

## Section

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

Fermat's Theorem | If f (c) is a local extrema and f is differentiable, then f ′(c) = 0. |

Mean Value Theorem | If f is differentiable and continuous on [a, b], then there exists c in [a, b] where, f'(c)=(f(b)-f(a))/(b-a) |

If f(x) is not continuous | f(x) can still have extreme values |

If f(x) is continuous but has no critical numbers on [a,b] | Then either f(a) or f(b) is the absolute minimum value |

If f has a secant line of slope 0 | Then f has a tangent line of slope 0 |

Local extrema occur where? | at critical points |

For a differentiable function on an interval... | There always exists a point whose instantaneous rate of change equals the average rate of change. |

Steps for solving related rates | 1) Draw a diagram and define the variables. 2) Find an equation relating those variables 3) Differentiate both sides of the equation from Step 2 with respect to t 4) solve for the unknown quantity |

Rectangle | A=L•W, P=2L + 2W |

Circle | Area=πr^2 Circumference=2πr |

Sphere | SA=4πr^2, V=4/3πr^3 |

Cylinder | SA=2πr^2+2πrh, V=πr^2h |

Cone | SA=πrh, V=π/3r^2h |

Cube | SA=6s^2, V=s^3 |

Distance formula | D^2=(x-x1)^2+(y-y1)^2 |

Open-Top Box Area | A=x^2+4xy |

Equilateral Triangle Area | A=√3/4s^2 |

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