Mathematics

Mathematics

Problem

For every pair of continuous functions f,g:[0,1]→Rf, g: [0, 1] \to R such that max⁡{f(x):x∈[0,1]}=max⁡{g(x):x∈[0,1]}\max \{f(x): x \in [0, 1]\} = \max \{g(x): x \in [0, 1]\}, which statement(s) is (are) correct? a. [f(c)]2+3f(c)=[g(c)]2+3g(c)[f(c)]^2 + 3f(c) = [g(c)]^2 + 3g(c) for some c∈[0,1]c \in [0, 1] b. [f(c)]2+f(c)=[g(c)]2+3g(c)[f(c)]^2 + f(c) = [g(c)]^2 + 3g(c) for some c∈[0,1]c \in [0, 1] c. [f(c)]2+3f(c)=[g(c)]2+g(c)[f(c)]^2 + 3f(c) = [g(c)]^2 + g(c) for some c∈[0,1]c \in [0, 1] d. [f(c)]2=[g(c)]2[f(c)]^2 = [g(c)]^2 for some c∈[0,1]c \in [0, 1]

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