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MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Minimax, Cubic Function

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School
UTSG
Department
Mathematics
Course
MAT135H1
Professor
Dimitri Chouchkov

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MAT135H1 verified notes
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25

MAT135H1 Lecture Notes - Lecture 25: Implicit Function, Searchlight, Pythagorean Theorem

29

MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Minimax, Cubic Function

30

MAT135H1 Lecture Notes - Lecture 30: Mean Value Theorem, Constant Function

Document Summary

Mat135 - lecture 29 - maximum and minimum values. We will begin to address it in this lecture and finish it next class. Given a function f on a domain d , find its largest and smallest values. Given f on an interval i , does f need . Since we have investigated this problem near the beginning of the term regarding intervals, we can conclude that to guarantee max and min on an interval i it is sufficient but not necessary to ask: Suppose f is continuous on the closed interval [ a , b ], then. F has both an absolute maximum and minimum on [ a , b ] At each local extremum, there is a horizontal tangent. This turns out to be a good but incomplete suggestion for this question. Maximum/minimum at c then either f ( c ) = 0 or f ( c ) does not exist.

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Related Questions

Supposeย f is a continuous function defined on a closed interval [a,b]

(a) What theorem guarantees the existence of an absolute maximum value and an absolute minimum value forย f?

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Calculus Maxima and Minima

Critical Points and Extreme Values

a) Find the critical points of the followingfunctions on the given interval.

b) Use a graphing utility to determine whether thecritical points correspond to local maxima, local minima, orneither.
c) Find the absolute maximum and minimum values on the giveninterval (if they exist)


f(t) = 3t/(t^2+1); [-2,2]


Please label all steps because I need to be able to figure outhow to do this type of problem on my own. Thanks!


Calculus Maxima and Minima


Critical Points and Extreme Values

a) Find the critical points of the followingfunctions on the given interval.

b) Use a graphing utility to determine whether thecritical points correspond to local maxima, local minima, orneither.
c) Find the absolute maximum and minimum values on the giveninterval (if they exist)


f(x) = x^2/3 (4-x^2); [-3,4]


Please label all steps because I need to be able to figure outhow to do this type of problem on my own. Thanks!