Question

Value of $\lambda$ for which the function $f\left(x\right)=2x^3-3(\lambda +2)x^2+12\lambda x$ has one local maxima and one local minima in $R$, can not be

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$f^{\prime }\left(x\right)=0$ must have two real and unequal roots
$\Rightarrow f^{\prime }\left(x\right)=6x^2-6(2+\lambda )x+12\lambda =6(x^2-(2+\lambda )x+2\lambda )$
$D>0\Rightarrow (2+\lambda {)}^2-8\lambda >0$
$\Rightarrow (\lambda -2{)}^2>0$
So $\lambda$ can not be $2$.