If Rolle's theorem holds for function f(x) = 2{x^3} + b{x^2} + cx,,x, ∈ ,left[ { - 1,1} right]

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5. Continuity and Differentiation

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If Rolle's theorem holds for the function $f(x) = 2{x^3} + b{x^2} + cx,\,x\, \in \,\left[ { - 1,1} \right]$ at the point $x = \frac{1}{2}$ , then $(2b+c)$ is equal to

A

$1$

B

$-1$

C

$2$

D

$-3$

Solution

$b=\frac{1}{2}, c=-2$

$\therefore \quad(2 b+c)=1+(-2)=-1$

(apply conditions of Rolle's theorem)

Standard 12

Mathematics

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