Find 'a' and 'b'. f(x) = { x2 + 3x + a , x< 1 and bx + 2 , x > 1 Share with your friends Share 11 Manbar Singh answered this I think your complete question is, Find the values of a and b iffx = x2+3x+a, x≤1bx+2, x > 1is differentiable at each x∈R.Here is the solution.RHD at x = 1 = limh→0f1+h-f1h⇒Rf'1 =limh→0 b1+h-1+3+ah⇒Rf'1 =limh→0b+bh-4-ah⇒Rf'1 =limh→0b = bLHD at x = 1 = limh→0f1-h-f1-h⇒Lf'1 =limh→01-h2+31-h+a-4-a-h⇒Lf'1 =limh→0h2-5h-h =limh→05-h = 5Since f is differentiable at x = 1, so Rf'1 = Lf'1⇒b = 5Since every differentiable function is continuous, so f is continuous at x = 1.Now, LHL = limx→0-fx = limx→0-x2+3x+aput x = 1-h, as x→1-, h→0LHL = limh→01-h2+31-h+a = limh→0h2-5h+4+a = 4+aRHL = limx→0+fx = limx→0+ bx+2put x = 1+h, as x→1+, h→0RHL = limh→0b1+h+2 = b+2Now, f1 = 4+aSince f is continuous at x = 1, thenLHL = RHL = f1⇒LHL = RHL⇒4+a = b+2⇒4+a = 5+2⇒a = 3 11 View Full Answer
