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If F Is Continuous Over the Closed Interval [1,4][ 1,4 ]

question 208

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If f is continuous over the closed interval [1,4][ 1,4 ] and differentiable over the open interval (1,4)( 1,4 ) , and that f(x)5f ^ { \prime } ( x ) \leq 5 for all x in [1,4][ 1,4 ] . If f(1)=2f ( 1 ) = 2 , what is the maximum possible value that f(4) can be?


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