The diagram shows part of the curve $$\(y=\frac{6}{x}\)$$. The points $$\((1,6)\)$$ and $$\((3,2)\)$$ lie on the curve. The shaded region is bounded by the curve and the lines $$\(y=2\)$$ and $$\(x=1\)$$. The tangent to the curve at a point $$\(X\)$$ is parallel to the line $$\(y+2 x=0\)$$. Show that $$\(X\)$$ lies on the line $$\(y=2 x\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：8(b)
Answer:
\[
\frac{d y}{d x}=\frac{-6}{x^{2}}
\]
\[
\frac{-6}{x^{2}}=-2 \rightarrow x=\sqrt{3}
\]
\(y=\frac{6}{\sqrt{3}}=2 \sqrt{3} \quad\) Lies on \(y=2 x\)
\frac{d y}{d x}=\frac{-6}{x^{2}}
\]
\[
\frac{-6}{x^{2}}=-2 \rightarrow x=\sqrt{3}
\]
\(y=\frac{6}{\sqrt{3}}=2 \sqrt{3} \quad\) Lies on \(y=2 x\)
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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