Find the values of `aa n db` so that the function `f(x)={x^2+3x+a ,ifxlt=1b x+2,ifx >1` is differentiable at each `x in Rdot`

Explanation

`f(x)=x^2+3x+a, for x<=1`

And`bx+2, for x>1`

The function is everywhere differentiable. So, it is also continuous.

Therefore,

Now,`lim_(x->1)f(x)=lim_(x->1^(+))f(x)`

`lim_(x->1)x^2+3x+a=lim_(x->1)bx+2`

`4+a=b+2`

`a−b=−2 ......(1)`

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