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For every pair of continuous functions \( f, g:[0,1] \rightarrow R \) such that \( \max \{f(x): x \in[0,1]\}=\max \{g(x): x \in[0,1]\} \),
\( \mathrm{P} \) the correct statement(s) is (are) :

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(A) \( (f(c))^{2}+3 f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
(B) \( (f(c))^{2}+f(c)=(g(c))^{2}+3 g(c) \) for some \( c \in[0,1] \)
(C) \( (f(c))^{2}+3 f(c)=(g(c))^{2}+g(c) \) for some \( c \in[0,1] \)
(D) \( (\mathrm{f}(\mathrm{c}))^{2}=(\mathrm{g}(\mathrm{c}))^{2} \) for some \( \mathrm{c} \in[0,1] \)
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