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 :

Question

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

Answer 1

F(-1)=F(1)  
Gives , b=-2

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

2a+b=-1