Maxima & Minima - Second Derivative Test| Ch 05 | Application Of Differentiation 08 Notes ; Polytechnic

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Maxima & Minima - Second Derivative Test| Ch 05 | Application Of Differentiation 07 Notes ; Polytechnic


Hey Everyone, How are you ... Today I will show you How to Solve Words Problem related to Maxima & Minima , which is chapter 06 , Application Of Differentiation ( Derivatives ), Which Is Module 02 Of Applied mathematics 02 

- Lecture 08 ( Topics ) :

1 ) Maxima & Minima - Words Problem. 

2 ) Some Important Questions 

3 ) Lecture Related Questions.



1 ) Maxima & Minima - Words Problem

- Step Required To Find Maxima & Minima ;

Step 01 ) F' ( x ) = 0 

Step 02 ) Determine extreme Points .

Step 03 ) Then Differentiate F'(x ) again And find second order derivatives.

Step 04 ) Then Put the extreme point On f''(x ) 

Case l ) F''(x) |x=C1 <0
C1 Point of Maxima

Case ll ) F'' (x ) | x = C2 > 0 

Case lll ) F''(x) |x=C2 = 0

- Go to first Derivative test Check the sign of F'(x ) 

Step 06 ) Then find maximum & Minimum value of function by put point of Maxima & Minima .

- Important Formula 


2 ) Some Important Questions 

Question 01 ) 

Find two positive number whose sum is 14 & Sum of whose square is minimum.

Solution : View On This Page 



Question 02 ) 

A Square Piece Of Tin of side 24cm is to be made into a box without top by cutting a square from each corner & Flolding up the flaps to form a box . What should be the side of square to be cut off so that the volume of the box is minimum ? also Find  this maximum volume .

Solution : View On This Page


Question 03 ) 

Show that height of closed cylinder of the given surface area & Maximum volume is equal to diameter of the base.

Solution : View On This Page



Question 04 ) 

A Wire of 28cm is cut into to pieces is made into square & other into circle , where should the wire be cut , so as to combinated area is minima.

Solution : View On This Page



Question 05 ) 

Show that the semi vertical angle of a cone of maximum value & Given Volume Slant  height is tan-¹√2

Solution : View On This Page





Maxima & Minima - Basic Concepts| Ch 05 | Lec 07 Notes ;-


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