Find the values of `a` and `b` so that the function `f(x)={x^2+3x+a , bx2` `,ifxlt=1ifx >1` is differentiable at each `xRdot`

Explanation

f is differentiable at `x=1`

`implies lim _{x -> 1^-} f’(x)= lim _{x -> 1^+} f’(x)`

`implies lim _{x -> 1^-} 2x+3=b`

`implies b=5`

f is continuous at `x=1`

`implies lim _{x -> 1^-} f(x)= lim _{x -> 1^+} f(x)`

`implies lim _{x -> 1^-} (x^2+3x+a)`= lim _{x -> 1^+} bx+2

`implies1+3+a= lim _{x -> 1^+} 5x+2`

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