At x=1 , the function f(x)= array cc x³-1, & 1 < x < x-1, & - < x 1 array . is

Step-by-step solution

f(x)= array cc x³-1, & 1 < x < x-1, & - < x 1 array . We have to check the continuity at x=1 . RHL _ x 1⁺ f(x)= _ x 1⁺ (x³-1 )=1-1=0 LHL _ x 1⁻ f(x)= _ x 1⁻ (x-1)=1-1=0f( l )=1-1=0 Thus the function is continuous at x=1 . f^ (x)= array cc 3 x², & 1 < x < 1, & - < x 1 array . Now, check the differentiability at x=1 . LHD at x=1 1 RHD at x=1 3(1)²=3A s, L H D R H D , function is not differentiable.