Good day! Thanks 3. (8 points) Let ( f:[a, b] longrightarrow mathbb{R} ) be continuous. (a) If ( f(x)0 ) for all ( x in[a, b] ), show that there exists ( m0 ) such that ( f(x)m ) for all ( x in[a, b] ).

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Good day! Thanks  3. (8 points) Let  ( f:[a, b]  longrightarrow  mathbb{R}  ) be continuous. (a) If  ( f(x)>0  ) for all  ( x  in[a, b]  ), show that there exists  ( m>0  ) such that  ( f(x)>m  ) for all  ( x  in[a, b]  ).

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(Solved): Good day! Thanks 3. (8 points) Let \( f:[a, b] \longrightarrow \mathbb{R} \) be continuous. (a) If ...

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