Question

If the function $f\left(x\right)=x^{3}-6x^{2}+ax+b$ satisfies all conditions of Rolle's theorem in $x\in \left[1,3\right],$ then the value of $a$ is equal to

• A. $1$
• B. $11$
• C. 22
• D. $2$

Answer 1

Answer: (B)

For Rolle’s theorem,
$f\left(1\right)=f\left(3\right)$
$\Rightarrow 1-6+a+b=27-54+3a+b$
$\Rightarrow 2a=22$
$\Rightarrow a=11$