## A rigorous treatment of maximum-minimum problems in the calculus |

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### Contents

Definitions | 1 |

Existence of Maxima and Minima | 2 |

Properties of Derivatives | 4 |

Copyright | |

7 other sections not shown

### Common terms and phrases

American Mathematical Monthly AP and PB approaches a limit backward derivative bank and walking Calculus circular cone closed bounded interval closed interval continuous function denote derivative equal equal to zero feet of fencing fence already standing fence of length field of largest Figure find the maximum finite or infinite function f(x g 0 g given interval global maximum greatest lateral area greatest volume hence independent variable inscribed angle interior point law of refraction least upper bound lim f(x logic involved maxima and minima maximum or minimum maximum V(X member of 22 miles per hour minimum of f(x MINIMUM PROBLEMS minute and walks monotonically one-quart tomato path APB pond of diameter positive proof of Theorem Proposition reader RIGOROUS TREATMENT second derivative set of values setting a derivative solution solving subintervals swimmer stands swims m yards upper bound Bo values taken wishes to reach x-axis yards per minute