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Question Number 123267 by mohammad17 last updated on 24/Nov/20

$$iff\left(x\right)=\mid 3-x\mid find{\left(f^2\right)}^{{}^{\prime }}\left(1\right)?$$

Commented by MJS_new last updated on 24/Nov/20

$$\mathrm{if}\mathrm{you}\mathrm{mean}{\left({\left(f\left(x\right)\right)}^2\right)}^{\prime }$$$${\left(f\left(x\right)\right)}^2={(3-x)}^2=x^2-6x+9$$$${\left({\left(f\left(x\right)\right)}^2\right)}^{\prime }=2x-6$$$$\mathrm{then}\mathrm{the}\mathrm{answer}\mathrm{is}-4$$

Answered by TANMAY PANACEA last updated on 24/Nov/20

$$f\left(x\right)=3-xwhen(3-x)>03>x$$$$f\left(x\right)=-3+xwhenx>3$$$$whenx<3(whenx=1)$$$$f\left(x\right)=3-x$$$$\frac{df}{dx}=-1$$$$\frac{d^{2}f}{{dx}^2}=0$$$$ithinkso$$$$$$

Answered by mathmax by abdo last updated on 24/Nov/20

$$\mathrm{f}\left(\mathrm{x}\right)=\mid \mathrm{x}-3\mid \Rightarrow {\mathrm{f}}^2\left(\mathrm{x}\right)={(\mathrm{x}-3)}^2={\mathrm{x}}^2-6\mathrm{x}+9\Rightarrow$$$${\left({\mathrm{f}}^2\right)}^{{}^{\prime }}\left(\mathrm{x}\right)=2\mathrm{x}-6\Rightarrow {\left({\mathrm{f}}^2\right)}^{{}^{\prime }}\left(1\right)=-4$$

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