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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
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B
-1
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C
2
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D
-2
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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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