Let f(x)= array cc a x(x+1)+b, & x 1 x-1 & 1 x 2 array . If the function f(x) is differentiable at x=1 , then what is the value of (a+b) ?

Step-by-step solution

Since, f ( x )= array cc ax ( x +1)+ b ; & x 1 x -1 ; & 1 x 2 array . Since, f(x) is differential at x=1 aligned & f ^ ( x )= array cc a (2 x +1) ; & x 1 1 ; & 1 x 2 array . & a (3)=1 a = 1 3 aligned since f(x) is continuous at x=1 2 a + b =0 ~b = -2 3 so, a+b= -1 x