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    Question

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    A (1,0) Correct Answer Incorrect Answer
    B (0,1) Correct Answer Incorrect Answer
    C (0,2) Correct Answer Incorrect Answer
    D (2,0) Correct Answer Incorrect Answer

    Solution

    The function is given by: (1)2 + a(1) + b = 2(1) +1 1 + a + b = 3 a + b = 2 Now, for differentiability at x=1, the left-hand derivative must be equal to the right-hand derivative. The derivative of x2 + ax + b is 2x + a. The derivative of 2x+1 is 2. Left-hand derivative at x=1: For differentiability, f′(1-) = f′(1+): 2+a=2 a=0 Now substitute the value of a into the continuity equation a + b = 2 0+ b=2 b=2 So, the values of a and b are a=0 and b=2. Therefore, (a,b)=(0,2).

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