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AP EAMCET201823 Apr 2018Morning ShiftMathematicsFunctionsActual

The maximum and minimum values of the function f:[R [R defined by f(x)=5 x+3 (x+ 3 )+8 for all x [R , are respectively.

Options

  1. A15, 1
  2. B8, - 8
  3. C-7, - 15
  4. D1, - 15

Correct answer

A. 15, 1

Step-by-step solution

aligned & f(x)=5 x+3 (x+ 3 )+8 & =5 x+3 [ x 3 - x 3 ]+8 & =5 x+3 [ 1 2 x- 3 2 x ]+8 & = 13 2 x- 3 3 2 x+8 aligned We know that, a x-b x is lie between [- a^2+b^2 , a^2+b^2 ] gathered - ( 13 2 )^2+ ( -3 3 2 )^2 +8 f(x) ( 13 2 )^2+ ( -3 3 2 )^2 +8 -7+8 f(x) 7+8 1 f(x) 15 gathered So, maximum value of f(x) is 15 and minimum value is 1 .

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