A point $$\(P\)$$ is moving along a curve in such a way that the $$\(x\)$$-coordinate of $$\(P\)$$ is increasing at a constant rate of 2 units per minute. The equation of the curve is $$\(y=(5 x-1)^{\frac{1}{2}}\)$$. Find the value of $$\(x\)$$ when the $$\(y\)$$-coordinate is increasing at $$\(\frac{5}{8}\)$$ units per minute. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：6(b)
Answer:
\(2 \times\) their \(\frac{5}{2}(5 x-1)^{-1 / 2}=\frac{5}{8}\) oe
\((5 x-1)^{1 / 2}=8\)
\(x=13\)
\((5 x-1)^{1 / 2}=8\)
\(x=13\)
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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