Question

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

A
1
B
-1
C
2
D
-2

Solution

## The correct option is A -1$$f(-1) = f(1)$$$$-2+a-b=2+a+b$$$$\Rightarrow b =-2$$$$f'(c)= 6{ c }^{ 2 }+2ac+b$$                              .$$f'(c)=0$$ at $$c=\dfrac{1}{2}$$ $$\Rightarrow a=\dfrac{1}{2}$$$$2a+b = -1$$Mathematics

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