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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let y=f(x) be a differentiable function such that f(3-x)=f(3+x) x R and the equation f(x)=0 has exactly 5 distinct real roots x₁, x₂, x₃, x₄ and x₅ . If x₁ < x₂ < x₃ < x₄ < x₅ , then which of the following is/are must be correct?

Options

  1. Ax₁+x₂+x₃+x₄+x₅=15
  2. Bf^ (x₃ )=0
  3. Cy=|f(x)| is not differentiable at x=x₁, x₂, x₄ and x₅ .
  4. Dy=|f(x)| is a differentiable function.

Correct answer

B. f^ (x₃ )=0

Step-by-step solution

f(3-x)=f(3+x) symmetric about x=3f (x₁ )=f (x₂ )=f (x₃ )=f (x₄ )=f (x₅ )=0 array ll & x₃=3 & x₁+x₂+x₃+x₄+x₅=15 & f^ (3)=0 array

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