The diagram shows part of the curve $$\(y=\frac{2}{(3-2 x)^{2}}-x\)$$ and its minimum point $$\(M\)$$, which lies on the $$\(x\)$$-axis. Find, by calculation, the $$\(x\)$$-coordinate of $$\(M\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：10(b)
Answer:
\(\frac{\mathrm{d} y}{\mathrm{~d} x}=0 \rightarrow(3-2 x)^{3}=8 \rightarrow 3-2 x=\mathrm{k} \rightarrow x=\)
\(\frac{1}{2}\)
Alternative method for question \(\mathbf{1 0}(\mathrm{b})\)
\(y=0 \rightarrow \frac{2}{(3-2 x)^{2}}-x=0 \rightarrow(x-2)(2 x-1)^{2}=0 \rightarrow x=\)
\(\frac{1}{2}\)
\(\frac{1}{2}\)
Alternative method for question \(\mathbf{1 0}(\mathrm{b})\)
\(y=0 \rightarrow \frac{2}{(3-2 x)^{2}}-x=0 \rightarrow(x-2)(2 x-1)^{2}=0 \rightarrow x=\)
\(\frac{1}{2}\)
Knowledge points:
1.7.4 locate stationary points and determine their nature, and use information about stationary points in sketching graphs. (Including use of the second derivative for identifying maxima and minima; alternatives may be used in questions where no method is specified.) (Knowledge of points of inflexion is not included.)
Solution:
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