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Manipal MET2010MathematicsContinuity and Differentiability

If f(x)= array cc a x^2+b, & 0 x 1 x+3, & 1 x 2 4, & x=1 array . , then the value of (a, b) for which f(x) cannot be continuous at x=1 is

Options

  1. A(2,2)
  2. B(3,1)
  3. C(4,0)
  4. D(5,2)

Correct answer

D. (5,2)

Step-by-step solution

We have, _ h 0 f(1-h)= _ h 0 a(1-h)^2+b=a+b _ h 0 f(1+h)= _ h 0 (1+h)+3=4 and f(1)=4 f(x) will not be continuous at x=1 , if a+b 4

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