Let $f:\left[a,b\right]\overrightarrow{1,\infty }$be a continuous function and let $g:R\vec{R}$be defined as$g\left(x\right)=\{0\text{if}xbThen$$g\left(x\right)$is continuous but not differentiable at a$g\left(x\right)$is differentiable on $R$$g\left(x\right)$is continuous but nut differentiable at $b$$g\left(x\right)$is continuous and differentiable at either $a$or $b$but not both.

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