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Question Number 214342 by issac last updated on 06/Dec/24

$$\mathrm{why}$$$$\mathrm{differantiable}f\to f\mathrm{is}\mathrm{continious}$$$$\mathrm{but}f\mathrm{is}\mathrm{continous}\nrightarrow \mathrm{differantiable}??$$

Commented by mr W last updated on 06/Dec/24

$$asmoothlineisalwayscontinous,$$$$butacontinouslineisnotalways$$$$smooth.$$

Commented by mr W last updated on 06/Dec/24

Commented by mr W last updated on 06/Dec/24

$$allarecontinious,butnotallare$$$$smooth\left(differentiable\right).$$

Answered by Frix last updated on 06/Dec/24

$$\mathrm{Just}\mathrm{think}\mathrm{of}\mathrm{an}\mathrm{example}:$$$$f\left(x\right)=\mid x\mid \mathrm{is}\mathrm{continuous}\mathrm{but}\mathrm{not}\mathrm{differentiable}$$$$\mathrm{at}x=0$$$$g\left(x\right)=\sqrt[3]{x^2-1}\mathrm{is}\mathrm{continuous}\mathrm{but}\mathrm{not}\mathrm{differentiable}$$$$\mathrm{at}x=\pm 1$$

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