Consider a differentiable \( f: R \rightarrow \) for which \( f^{\prime}(0)=\ln 2 \) and \( f \)...

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Consider a differentiable \( f: R \rightarrow \) for which \( f^{\prime}(0)=\ln 2 \) and \( f \) \( (x+y)=2^{x} f(y)+4^{y} f(\mathrm{x}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R} \). Which of the following is(are) correct
(a) \( f(4)=240 \)
(b) \( f^{\prime}(2)=24 \ln 2 \)
(c) The minimum value of \( y=f(x) \) is \( -\frac{1}{2 \mathrm{f}(1)} \)
(d) The number of solution of \( f(x)=2 \) is 1
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