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Q.
The smallest positive integral value of $a$ , such that the function $f\left(x\right)=x^{4}-4ax^{2}+10$ has more than two local extrema, is
NTA AbhyasNTA Abhyas 2022
Solution:
$f^{'} \left(x\right) = 4 x^{3} - 8 a x$
$=4x\left(x^{2} - 2 a\right)$
$=4x\left(x - \sqrt{2 a}\right)\left(x + \sqrt{2 a}\right)$
Hence, $f\left(x\right)$ has $3$ local extrema if $\sqrt{2 a}$ is real i.e., $2a>0\Rightarrow a>0$
$\therefore $ Value of minimum $a=1$