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AP EAMCET201923 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

Let (f ) be a polynomial function defined on ([2,7] ). If (f(2)=3 ) and (f^ (x) 5 ) for all (x ) in ((2,7) ), then the maximum possible value attained by (f ) at (x=7 ) is

Options

  1. A7
  2. B14
  3. C18
  4. D28

Correct answer

D. 28

Step-by-step solution

Since, the polynomial function are continuous and differentiable in interval (R ). So, according to Lagranage's mean value theorem ( aligned & f(7)-f(2) 7-2 =f^ (x) 5 (given) & f(7)-f(2) 25 f(7) 28 aligned ) Hence, option (d) is correct.

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