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Question Number 167567 by pete last updated on 19/Mar/22

$$\mathrm{Find}\mathrm{the}\mathrm{coordinates}\mathrm{of}\mathrm{the}\mathrm{point}\mathrm{on}\mathrm{the}$$$$\mathrm{curve}\mathrm{y}={3\mathrm{x}}^2-2\mathrm{x}-5,\mathrm{where}\mathrm{the}\mathrm{tangent}$$$$\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{line}\mathrm{y}-5=8\mathrm{x}.$$

Commented by greogoury55 last updated on 19/Mar/22

$$y^{\prime }=8$$$$6x-2=8\Rightarrow x=\frac{5}{3}$$$$y=3\left(\frac{25}{9}\right)-2\left(\frac{5}{3}\right)-5$$$$y=\frac{25-10-15}{3}=0$$$$thepoint(\frac{5}{3},0)$$

Commented by pete last updated on 19/Mar/22

$$\mathrm{Thanks}\mathrm{for}\mathrm{your}\mathrm{time},\mathrm{sir}$$

Commented by otchereabdullai@gmail.com last updated on 21/Mar/22

$$\mathrm{nice}!$$

Answered by som(math1967) last updated on 19/Mar/22

$$slopeofy=8x+5is8$$$$\therefore slopeoftangentalso8$$$$nowy=3x^2-2x-5$$$$\frac{dy}{dx}=6x-2\therefore 6x-2=8\Rightarrow x=\frac{10}{6}=\frac{5}{3}$$$$\therefore y=3\times \frac{25}{9}-\frac{10}{3}-5=5-5=0$$$$\therefore pointis(\frac{5}{3},0)$$$$$$$$$$

Commented by pete last updated on 19/Mar/22

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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