The distance travelled by a particle upto time \( x \) is given by \( f(x)=x^{3}-2 x+1 \). The t...

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The distance travelled by a particle upto time \( x \) is given by \( f(x)=x^{3}-2 x+1 \). The time \( c \) at which the velocity of the particle is equal to its average velocity between times \( x=1 \) \( \sec \) and \( x=2 \sec \), is
(A) \( 15 \mathrm{sec} \)
(B) \( \sqrt{\frac{3}{2}} \sec \)
(C) \( \sqrt{3} \mathrm{sec} \)
(D) \( \sqrt{\frac{7}{3}} \sec \)
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