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AP EAMCET201921 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

The maximum value of the function f(x)= (x+ 2 3 )- (x+ 6 )+ (x+ 6 ) in [- 5 12 , - 3 ] is

Options

  1. A11 2 6
  2. B11 3 6
  3. C3
  4. D1

Correct answer

B. 11 3 6

Step-by-step solution

Given, aligned & f(x)= (x+ 2 3 )- (x+ 6 )+ (x+ 6 ) & A- B= (A-B) A B aligned aligned & (x+ 2 3 )- (x+ 6 ) & = 2 (x+ 2 3 ) (x+ 6 ) & aligned Now, aligned f(x) & = 1 2 2 (x+ 2 3 ) (x+ 6 ) + (x+30^ ) & = 2 (150^ +2 x )+ 90^ + (x+30^ ) & = (x+30^ )- 2 (2 x-30^ ) aligned Differentiate w.r.t. x , we get f^ (x)=- (x+30^ )- 4 (2 x-30^ ) ^2 (2 x-30^ ) Since, it lie -75^ 0 for all -75^ < x < -60^ So, f_ at x=-60^ f (-60^ )= (60^ )- (-30^ )+ (-30^ )= 3 + 3 3 + 3 2 = 6 3 +2 3 +3 3 6 = 11 3 6

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