JEE Main & Advanced Mathematics Applications of Derivatives Properties of Maxima and Minima

Properties of Maxima and Minima

Category : JEE Main & Advanced

(i) Maxima and minima occur alternately, that is between two maxima there is one minimum and vice-versa.

 

 

(ii) If \[f(x)\to \infty \]as \[x\to a\] or \[b\] and \[f'(x)=0\] only for one value of \[x\] (say \[c\]) between \[a\] and \[b,\] then \[f(c)\] is necessarily the minimum and the least value.

 

 

If \[f(x)\to -\infty \] as \[x\to a\] or \[b,\] then \[f(c)\] is necessarily the maximum and the greatest value.

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