Let `f:[a , b]vec[1,oo)` be a continuous function and let `g: RvecR` be defined as `g(x)={0ifx bT h e n` `g(x)` is continuous but not differentiable at a `g(x)` is differentiable on `R` `g(x)` is continuous but nut differentiable at `b` `g(x)` is continuous and differentiable at either `a` or `b` but not both.