Let f(x)= array l |x|,- < x < 2 |2 x-4|, 2 x 20 array .x=a is a point where f(x) is continuous but not differentiable and x=b is a point where f(x) is not differentiable (a b) . Then, a+b=

Step-by-step solution

aligned |x|= array cc -x, & if x < 0 x, & if x 0 array and |2 x-4|= array cc 2 x-4, & if x 2 -(2 x-4), & if x < 2 array . aligned f(x)= array ccc -x & , & - < x < 0 x & , & 0 x < 2 2 x-4 & , & 2 x 20 array . At x=0 aligned & LHL = _ RHL = ^x _ x 0⁻ f(x)=0 & f(0)=0 aligned f(x) is continuous at x=0 At x=2 aligned & LHL = _ x 2⁻ f(x)=2 & RHL = _ x 2⁺ f(x)=0 aligned f(x) is not continuous at x=2 f^ (x)= array cc -1, & - < x < 0 1, & 0 x < 2 2, & 2 x 20 array . The function is not differentiable at both the points x=0