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Question Number 122393 by benjo_mathlover last updated on 16/Nov/20

$$f\left(x\right)=x\mid x-1\mid \Rightarrow f{}^{\prime }\left(1\right)=?$$

Answered by MJS_new last updated on 16/Nov/20

$$\mathrm{does}\mathrm{not}\mathrm{exist}$$

Answered by Bird last updated on 17/Nov/20

$${lim}_{h\to 0^{+}}\frac{f(1+h)-f\left(1\right)}{h}$$$$={lim}_{h\to o^{+}}\frac{(1+h)h}{h}={lim}_{h\to 0^{+}}1+h=1$$$${lim}_{h\to 0^{-}}\frac{f(1+h)-f\left(1\right)}{h}$$$$={lim}_{h\to 0^{-}}\frac{(1+h)(-h)}{h}={lim}_{h\to 0^{-}}-(1+h)$$$$=-1itsclearthstfisnotderivable$$$$at1\Rightarrow f^{{}^{\prime }}\left(1\right)dontexist$$

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