Question

If Rolle’s theorem holds for the function f(x) = 2x³ + bx² + cx, x ∈ −[1 ,1] , at the point x = 1/2, then 2b + c equals

(A)  1

(B)  −1

(C)   2

(D)  −3

Answer 1

Correct option (B) −1

Explanation :

f(−1) = f(1) and f'(1/2) = 0 ⇒ −2 + b - c = 2 + b + c ⇒ c = −2

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