The second degree polynomial \( f(x) \), satisfying \( f(0)=0 \), \( f(1)=1, f^{\prime}(x)0 \for...
The second degree polynomial \( f(x) \), satisfying \( f(0)=0 \), \( f(1)=1, f^{\prime}(x)0 \forall x \in(0,1) \quad \) [One Correct Option, 2005]
(a) \( f(x)=\phi \)
(b) \( f(x)=a x+(1-a) x^{2}, \forall a \in(0, \infty) \)
(c) \( f(x)=a x+(1-a) x^{2}, a \in(0,2) \)
(d) No such polynomial
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