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  4. The function f(x)=2x3-3(a + b)x2+6abx has a local maximum at x=a, if

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Q. The function $f\left(x\right)=2x^{3}-3\left(a + b\right)x^{2}+6abx$ has a local maximum at $x=a,$ if

NTA AbhyasNTA Abhyas 2022

Solution:

$f^{'} \left(x\right) = 6 \left(x^{2} - \left(a + b\right) x + a b\right)$
$=6\left(x - a\right)\left(x - b\right)$
Solution
i.e. $f\left(x\right)$ has local maximum at $x=a$ if $a < b$