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If F Is Continuous Over [1,3][ 1,3 ] And Differentiable Over (1,3)( 1,3 )

Question 179

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If f is continuous over [1,3][ 1,3 ] and differentiable over (1,3)( 1,3 ) , suppose that 2f(x)52 \leq f ^ { \prime } ( x ) \leq 5 for all x in [1,3][ 1,3 ] , and f(1)=4f ( 1 ) = 4 . What is the maximum possible value that f(3) can be? What is the minimum possible value that f(3) can be?

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