For a real parameter

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

k

, define

f_k(x)=x^{3}-2kx+k

on the interval

[0,2]

. For which values of

k

is at least one real solution of

f_k(x)=0

guaranteed to occur in

(0,2)

? (a)

0<k<\dfrac{8}{3}

(b) All\ real\ k (c)

k<0\text{ or }k>\dfrac{8}{3}

(d)

k\le 0\text{ or }k\ge \dfrac{8}{3}