\( f(x), g(x), h(x) \) all are continuous and differentiable functions in \( [a, b] \) also \( a...

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\( f(x), g(x), h(x) \) all are continuous and differentiable functions in \( [a, b] \) also \( acb \) and \( f(a)=g(a)=h(a) \). Point of intersection of the tangent at \( x=c \) with chord joining \( x=a \) and \( x=b \) is on the left of \( c \) in \( y=f(x) \) and on the right in \( y=h(x) \). And tange.lt at \( x=c \) is parallel to the chord in case of \( y=g(x) \).
Now, answer the following questions.
If \( c=\frac{a+b}{2} \) for each \( b \), then
(a) \( g(x)=A x^{2}+B x+C \)
(b) \( g(x)=\log x \)
(c) \( g(x)=\sin x \)
(d) \( g(x)=e^{x} \)
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