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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

6 years ago


Answers : (2)


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

6 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                      

6 years ago

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