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  4. If f(x)=((x3-3 x+6)(x-α)/2(x-α)) has range as R( set of real numbers), then α can be

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Q. If $f(x)=\frac{\left(x^3-3 x+6\right)(x-\alpha)}{2(x-\alpha)}$ has range as $R($ set of real numbers), then $\alpha$ can be

Application of Derivatives

Solution:

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$\frac{x^3-3 x+6}{2}=4 \Rightarrow x=-1,2$ and $\frac{x^3-3 x+6}{2}=2 \Rightarrow x=1,-2$
$\Rightarrow$ For range to be R, $\alpha \in[-2,2]$