Question

Let $f\left(x\right)=2x^3-3(a+1)x^2+6ax-12$has maxima and minima at $x_1$ and $x_2$ respectively and if $2x_1=x_2$, then the value of $a$ is

• A. $1$
• B. $\frac{1}{3}$
• C. $-1$
• D. $2$

Answer 1

The correct option is D $2$

$f^{\prime }\left(x\right)=6(x-1)(x-a)$
If $a<1$, then $x_1=a$ is point of maxima
and $x_2=1$ is point of minima
Hence, $a=\frac{1}{2}$
If $a>1$, then $x_1=1$ is point of maxima
and $x_2=a$ is point of minima
Hence, $a=2$