If the function f x = x 3 - 6 x 2 + a x + b satisfies all conditions of Rolle's theorem in x ∈ 1,3 , then the value of a is equal to

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Question: Answered & Verified by Expert

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

MathematicsApplication of DerivativesJEE Main

Options:

A $1$
B $11$
C 22
D $2$

Solution:

1816 Upvotes Verified Answer

The correct answer is:

11

For Rolle’s theorem,

f (1) = f (3)

\Rightarrow 1 - 6 + a + b = 27 - 54 + 3 a + b

\Rightarrow 2 a = 22

\Rightarrow a = 11

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