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Manipal MET2014MathematicsContinuity and Differentiability

The function f(x)= (x^2-1 ) |x^2-3 x+2 |+ |x| is non-differentiable at

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

we know that function |x| is not differentiable at aligned & x=0 & |x^2-3 x+2 |=|(x-1)(x-2)| aligned Hence, it is not differentiable at x=1 and 2 Now, f(x)= (x^2-1 ) |x^2-3 x+2 |+ |x| is not differentiable at x=2 . For 1 x 2, f(x)=- (x^2-1 ) (x^2-3 x+2 )+ x For 2 x 3, f(x)= (x^2-1 ) (x^2-3 x+2 )+ xL f^ (x)=- (x^2-1 )(2 x-3)-2 x (x^2-3 x+2 )- xL^ (2)=-3 2 aligned & R f^ (x)= (x^2-1 )(2 x-3)+2 x (x^2-3 x+2 )- x & R^ (2)=(4-1)(4-3)+0- 2=3- 2 aligned Hence, L^ (2) R f^ (2) . So, f(x) is not differentiable at x=2 .

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