LET’S BRUSH UP WITH MAXIMA

Do problems on Maxima and Minima haunt you ? So please stop nightmaring it.And go through the article.Try to get into the thorough concept. Before starting doing sums related to maxima and minima. let’s have a brief tour over the basics of Maxima and Minima..( I ) A function,f (x) attains its maximum value at point x = c When f (c h ) – f (c ) < 0 ,[ where h is a very small increment to c] And f (c- h ) – F ( c ) < 0 ( II) And f(x ) attains its minimum value at point x = c When f (c h ) – f ( c ) > 0 And f (c – h ) – f ( c ) > 0And now the problem is how to determine whether the function attains its maximum or mininimum value at point c and also how to determine the value of point c.The steps involve to find out the above is described below (1 ) 1st of all we have to find f ‘ (x) and f “ (x) [ Where f ‘(x ) = dy/ dx , and f “ ( x ) = d²x / dy² ] ( 2 ) Then we have to equate f ‘ ( x ) = 0 and have to sove out the corresponding value(s ) of x ., Let they be c1 and c 2. (3 ) Now have to find the f “ ( c1 ) and f ( c 2 ) ( 4 ) now if f” ( c1 ) > 0 ;the function will attain the minimum value at x = c1 And if f “ ( c 2 ) < 0 ; the function will attain the maximum value = c2 Now we will try to relate the above when solving problems based on maxima and minima.(a) Find the turning point(s) of the following function and atain it is maximum

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