A curve is such that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{6}{(3 x-2)^{3}}\)$$ and $$\(A(1,-3)\)$$ lies on the curve. A point is moving along the curve and at $$\(A\)$$ the $$\(y\)$$-coordinate of the point is increasing at 3 units per second. Find the rate of increase at $$\(A\)$$ of the $$\(x\)$$-coordinate of the point. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_m21_qp_12 Year：2021 Question No：6(a)
Answer:
At \(x=1, \frac{\mathrm{d} y}{\mathrm{~d} x}=6\)
\(\frac{\mathrm{d} x}{\mathrm{~d} t}=\left(\frac{\mathrm{d} x}{\mathrm{~d} y} \times \frac{\mathrm{d} y}{\mathrm{~d} t}\right)=\frac{1}{6} \times 3=\frac{1}{2}\)
\(\frac{\mathrm{d} x}{\mathrm{~d} t}=\left(\frac{\mathrm{d} x}{\mathrm{~d} y} \times \frac{\mathrm{d} y}{\mathrm{~d} t}\right)=\frac{1}{6} \times 3=\frac{1}{2}\)
Knowledge points:
1.7.3 apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (Including connected rates of change, e.g. given the rate of increase of the radius of a circle, find the rate of increase of the area for a specific value of one of the variables.)
Solution:
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