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Find 'a' and 'b', if the function given ...

Find 'a' and 'b', if the function given by:
`f(x)={{:(ax^(2)+b", if "xlt1),(2x+1", if "xge1):}`
is differentiable at x = 1.

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Knowledge Check

  • The values of a and b such that the function f defined as f(x)={{:(ax^(2)-b",",,|x|lt1),(-1//|x|",",,|x|ge1):} is differentiable are

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    B
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    D
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  • The function f(x)={(e^(2x)-1, x lt0),(ax^2+(bx^2)/2-1, xge0):} continuous and differentiable for

    A
    a=1, b=2
    B
    a=2, b=1
    C
    a=2, any b
    D
    any a, b=4

  • Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2, xlt1),(bx+a^(2),xge1):} is differentiable of all xepsilonR , then

    A
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    C
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