In the interval [0,3] , the function f(x)=|x-1|+|x-2| is

Step-by-step solution

f(x)=|x-1|+|x-2|, x [0,3] array l f(x)= array cc -2 x+3, & x 1 1, & 1 x 2 2 x-3, & x 2 array . _ x 1⁻ f(x)=1 and _ x 1⁺ f(x)=1, f(1)=1 f(x) is continous at x=1 array f(x) is not differentiable at x=1 Similarly, _ x 2⁺ f^ (x)=2, _ x 2⁻ f^ (x)=0 f(x) is not differentiable at x=2