Answer :

Given that, is differentiable at x = 1.


We know that,f(x) is differentiable at x =1 Lf’(1) = Rf’(1).


Lf’(1) =


=


= ( f(x) = x2+3x+p, if x≤ 1)


=


=


=


=


= 5


Rf’(1) =


=


= ( f(x) = qx+2, if x > 1)


=


=


=


=q


Since, Lf’(1) = Rf’(1)


5 = q (i)


Now, we know that if a function is differentiable at a point,it is necessarily continuous at that point.


f(x) is continuous at x = 1.


f(1-) = f(1+) = f(1)


1+3+p = q+2 = 1+3+p


p-q = 2-4 = -2


q-p = 2


Now substituting the value of ‘q’ from (i), we get


5-p = 2


p = 3


p = 3 and q = 5


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