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Question Number 12013 by tawa last updated on 09/Apr/17
The slope of a curve is, 7x + 3  and it passes through the point (2, 4),  Find the equation of the point
$$\mathrm{The}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{is},\:\mathrm{7x}\:+\:\mathrm{3}\:\:\mathrm{and}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:\mathrm{4}\right), \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$
Answered by ajfour last updated on 09/Apr/17
(dy/dx)=7x+3  ∫dy=∫(7x+3)dx  ⇒ y=((7x^2 )/2)+3x+C  as it passes through (2,4)       4=((7×4)/2)+3×2+C  ⇒ C=4−20=−16     y=((7x^2 )/2)+3x−16 .
$$\frac{{dy}}{{dx}}=\mathrm{7}{x}+\mathrm{3} \\ $$$$\int{dy}=\int\left(\mathrm{7}{x}+\mathrm{3}\right){dx} \\ $$$$\Rightarrow\:{y}=\frac{\mathrm{7}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{3}{x}+{C} \\ $$$${as}\:{it}\:{passes}\:{through}\:\left(\mathrm{2},\mathrm{4}\right) \\ $$$$\:\:\:\:\:\mathrm{4}=\frac{\mathrm{7}×\mathrm{4}}{\mathrm{2}}+\mathrm{3}×\mathrm{2}+{C} \\ $$$$\Rightarrow\:{C}=\mathrm{4}−\mathrm{20}=−\mathrm{16} \\ $$$$\:\:\:{y}=\frac{\mathrm{7}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{3}{x}−\mathrm{16}\:. \\ $$
Commented by tawa last updated on 09/Apr/17
God bless you sir.
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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