If the function f(x)=x3-6x2+ax+b satisfies all conditions of Rolle's theorem in x∈ [1,3], then the value of a is equal to

Question

If the function f(x)=x3-6x2+ax+b satisfies all conditions of Rolle's theorem in x∈ [1,3], then the value of a is equal to (A) 1 (B) 11 (C) 22 (D) 2

Tardigrade Admin · Accepted Answer

For Rolle’s theorem, f(1)=f(3) ⇒ 1-6+a+b=27-54+3a+b ⇒ 2a=22 ⇒ a=11

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