For every pair of continuous functions $\mathrm{f}, \mathrm{g}:[0,1] \rightarrow \mathrm{R}$ such that $\max \{f(x): x \in[0,1]\}=\max \{g(x): x \in[0,1]\}$, the correct statement(s) is (are) :
Select ALL correct options:
A
$(f(c))^2+3 f(c)=(g(c))^2+3 g(c)$ for some $c \in[0,1]$
B
$(\mathrm{f}(\mathrm{c}))^2+\mathrm{f}(\mathrm{c})=(\mathrm{g}(\mathrm{c}))^2+3 \mathrm{~g}(\mathrm{c})$ for some $\mathrm{c} \in[0,1]$
C
$(\mathrm{f}(\mathrm{c}))^2+3 \mathrm{f}(\mathrm{c})=(\mathrm{g}(\mathrm{c}))^2+\mathrm{g}(\mathrm{c})$ for some $\mathrm{c} \in[0,1]$
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