The sum of absolute maximum and absolute minimum values of the function f x = 2 x 2 + 3 x - 2 + sin x cos x…

The sum of absolute maximum and absolute minimum values of the function fx=2x2+3x-2+sinxcosx in the interval 0,1 is
  1. 3+sin1cos2122
  2. 3+121+2cos1sin1
  3. 5+12sin1+sin2
  4. 2+sin12cos12

Solution

Given fx=2x2+3x-2+sinxcosx

⇒fx=2x-1x+2+sinxcosx

Now, f'x=4x+3+cos2x4,12<x<1-4x+3+cos2x4,0≤x<12

For 0≤x<12⇒f'x<0

For 12<x≤1⇒f'x>0

So fx has minima at x=12 and maxima at x=1

Hence, f12+f1=3+121+2cos1sin1

Asked in: JEE Main 2022 (24 Jun Shift 1)

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