Q. 795.0( 2 Votes )
Given that, is differentiable at x = 1.
We know that,f(x) is differentiable at x =1 ⇔ Lf’(1) = Rf’(1).
= (∵ f(x) = x2+3x+p, if x≤ 1)
= (∵ f(x) = qx+2, if x > 1)
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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