Question Number 175395 by infinityaction last updated on 29/Aug/22
![f(4) = (1/4) and f(8) = (1/2) ∫_4 ^8 (( [f′(x)]^2 )/([f(x)]^4 ))dx = 1 then f(6)= ?](https://www.tinkutara.com/question/Q175395.png)
$$\:\:\:\:\:{f}\left(\mathrm{4}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:{and}\:\:\:\:{f}\left(\mathrm{8}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\int_{\mathrm{4}} ^{\mathrm{8}} \:\frac{\:\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{\left[{f}\left({x}\right)\right]^{\mathrm{4}} }{dx}\:\:=\:\:\mathrm{1}\:\:\:\:{then}\:\:\:{f}\left(\mathrm{6}\right)=\:? \\ $$