JEE Mains · Maths · STD 12 - 5. continuity and differentiation
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 \(1\)
Answer & Solution
Correct Answer
(B) \(-1\)
Step-by-step Solution
Detailed explanation
Conduction for Rolls theorem \(f(1)=f(-1)\) and \(f^{\prime}\left(\frac{1}{2}\right)=0\) \(c=-2\) and \(b=\frac{1}{2}\) \(2 b+c=-1\)
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