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considering f(x) is a twice differentiable function if f ' (a) =0 and f '' (a) 0 it said to be minima but sometimes this rule failed to work can u tell me why

considering f(x) is a twice differentiable function


if f ' (a) =0  and f '' (a) <0 it is said to be maxima similary if f ''(a)>0 it said to be minima but sometimes this rule failed to work can u tell me why

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2 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

repeatedly differentiate the function till you get the smallest value of n for which fn(x)≠zero, if n is even and the  derivative is positive it is a minimum, if the derivative is negative you get a maximum,if n is odd, it is neither a maximum nor a minimum

charu shikha
14 Points
10 years ago

It is called second order derivative test it is used to check whether the obtained answer is maxima or minima but sometimes we get f "(a)=0 so here it fails in this case nth order derivative test is used                      

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