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If f x = a x + b ,  if  x ≤ 1 a x 2 + c ,  if  1 < x ≤ 2 d x 2 + 1 x ,  if  x ≥ 2 is differentiable on R , then a d - b c =

Options

  1. A0
  2. B1
  3. C- 1
  4. D2

Correct answer

C. - 1

Step-by-step solution

Given: f x = a x + b ,  if  x ≤ 1 a x 2 + c ,  if  1 < x ≤ 2 d x 2 + 1 x ,  if  x ≥ 2 is differentiable on R So f x should be continuous on R Now continuity at x = 1 f 1 - = f 1 + = f 1 ⇒ a + b = a + c ⇒ b = c     . . . i Now continuity at x = 2 f 2 - = f 2 + = f 2 ⇒ 4 a + c = 4 d + 1 2 = 8 a + 2 c = 4 d + 1   . . . ii Now f ' x = a ,  if  x ≤ 1 2 a x ,  if  1 < x ≤ 2 d x 2 - 1 x 2 ,  if&#16

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