Maxima and minima problems with solutions pdf

6.08  ·  1,313 ratings  ·  271 reviews
maxima and minima problems with solutions pdf

Maxima/Minima Problems - Mathematics LibreTexts

The local maxima are the largest values maximum that a function takes in a point within a given neighborhood. The local minima are the smallest values minimum , that a function takes in a point within a given neighborhood. The number f c is called the maximum value of f on D. The maximum and minimum values of f are called the extreme values of f. Using the Product Rule , we get. So, the critical numbers are and 0. How to find all the critical values of a function?
File Name: maxima and minima problems with solutions
Size: 23152 Kb
Published 17.01.2019

Word Problem - Maximum/Minimum Value

21 - 24 Solved problems in maxima and minima

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Published on Jun 1, SlideShare Explore Search You.

Local maximum and minimum points are quite distinctive on the graph of a function, and are therefore useful in understanding the shape of the graph. In many applied problems we want to find the largest or smallest value that a function achieves for example, we might want to find the minimum cost at which some task can be performed and so identifying maximum and minimum points will be useful for applied problems as well. Some examples of local maximum and minimum points are shown in figure 5. This is important enough to state as a theorem, though we will not prove it. Theorem 5.


Please Visit our new Website here. Contact mokshya gmail. Did you send Friend request to Professor Subhashish Chattopadhyay? Everything can be searched in the net. Someone can know and find; if he wants to. Yet information at a single place helps. In fact organized information communicates much better.

Where does it flatten out? Where the slope is zero. Where is the slope zero? The Derivative tells us! Using derivatives we can find the slope of that function:. A derivative basically finds the slope of a function.

Problem 1: 3. Sketch the graph of a function which is continuous on [1, 5], and has all the following properties: It has an absolute maximum at 5. It has an absolute minimum at 2. It has a local maximum at 3. It has local minima at 2 and at 4. Solutions There are, of course, very many dierent ways of doing this problem.


  1. Anbardiman says:

    In mathematical analysis , the maxima and minima the respective plurals of maximum and minimum of a function , known collectively as extrema the plural of extremum , are the largest and smallest value of the function, either within a given range the local or relative extrema or on the entire domain of a function the global or absolute extrema.

  2. Let G. says:

    These are the tests to justify your answers: ′′ Maxima and Minima Problems o Read the on each side of your solution, if the first derivative is too.

  3. Yves F. says:


Leave a Reply

Your email address will not be published. Required fields are marked *