Lf Rolle's theorem holds for function f(x) =2x^3 + bx^2 + cx, x ∈ [-1, 1], at point x =

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5. Continuity and Differentiation

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lf Rolle's theorem holds for the function $f(x) =2x^3 + bx^2 + cx, x \in [-1, 1],$ at the point $x = \frac {1}{2},$ then $2b+ c$ equals

A

$-3$

B

$-1$

C

$2$

D

$1$

(JEE MAIN-2015)

Solution

Conduction for Rolls theorem

$f(1)=f(-1)$

and $f^{\prime}\left(\frac{1}{2}\right)=0$

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

$2 b+c=-1$

Standard 12

Mathematics

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