Let \( f(x) \) be twice differentiable function such that \( f^{\prime \prime}(x)0 \) in \( [0,2...
Let \( f(x) \) be twice differentiable function such that \( f^{\prime \prime}(x)0 \) in \( [0,2] \). Then :
(a) \( f(0)+f(2)=2 f(c) \), for atleast one \( c, c \in(0,2) \)
(b) \( f(0)+f(2)2 f(1) \)
(c) \( f(0)+f(2)2 f(1) \)
(d) \( 2 f(0)+f(2)3 f\left(\frac{2}{3}\right) \)
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