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# If the Rolle's theorem holds for the function $\;f(x) = 2x^{3}+ax^{2}+bx\;$ in the interval $\; [-1 ,1]\;$ for the point $\;c=\large\frac{1}{2}\;$ then the value of 2a+b is :

$(a)\;1\qquad(b)\;-1\qquad(c)\;2\qquad(d)\;-2$

F(-1)=F(1)
Gives , b=-2

Also, f'(1/2)=0
Gives a=1/2

2a+b=-1