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Question Number 50161 by cesar.marval.larez@gmail.com last updated on 14/Dec/18

$$Findthefunctionwhosefirst$$$$derivativeis8-\frac{5}{\sqrt[3]{x^2}}theinitial$$$$conditionsf\left(8\right)=-20$$

Answered by afachri last updated on 14/Dec/18

$$F\left(x\right)=\int f^{\prime }\left(x\right)dx$$$$=\int 8-5x^{-\frac{2}{3}}dx$$$$=8x-\left(\frac{5}{(-\frac{2}{3}+1)}\right)x^{-\frac{2}{3}+1}+C$$$$=8x-15x{}^{\frac{1}{3}}+C$$$$\mathrm{to}\mathrm{find}C:$$$$F\left(8\right)=-20$$$$8\left(8\right)-15{\left(8\right)}^{\frac{1}{3}}+C=-20$$$$64-30+C=-20$$$$C=-54$$$$$$$$\mathrm{So}:F\left(x\right)=8x-15x^{\frac{1}{3}}-54$$$$$$$$$$

Commented by cesar.marval.larez@gmail.com last updated on 14/Dec/18

$$wowfriendmyrespectiwilltheothers$$

Commented by afachri last updated on 14/Dec/18

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{been}\mathrm{our}\mathrm{pleasure}$$

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