A curve is such that $$$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{6}{(3 x-2)^{3}}$$$ and $$$A(1,-3)$$$ lies on the curve. A point is moving along the curve and at $$$A$$$ the $$$y$$$-coordinate of the point is increasing at 3 units per second. Find the equation of the curve. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_12 Year：2021 Question No：6(b)

Answer:

$[y=]\left(\frac{6(3 x-2)^{-2}}{-2}\right) \div(3)[+c]$
$-3=-1+c$
$y=-(3 x-2)^{-2}-2$