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Let x = 1 2 and x = 1 are the extreme points of f x = a l o g x + b x x + 2 c o s π x π , then

Options

  1. Aa - b = 2
  2. Ba + b = 1
  3. Ca b = 1 2
  4. Da b = 2

Correct answer

A. a - b = 2

Step-by-step solution

f ' x = a x + 2 b x - 2 s i n π x Now f ' 1 2 = 0 ⇒ 2 a + b - 2 = 0 & f ' 1 = 0 ⇒ a + 2 b = 0 ⇒ b = - 2 3 and a = 4 3

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