The diagram shows the curve with equation $$\(y=\frac{x-2}{x^{2}+8}\)$$. The shaded region is bounded by the curve and the lines $$\(x=14\)$$ and $$\(y=0\)$$. Find $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ and hence determine the exact $$\(x\)$$-coordinates of the stationary points. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：4(a)
Answer:
Differentiate using quotient rule (or product rule)
\(\operatorname{Obtain} \frac{\left(x^{2}+8\right)-2 x(x-2)}{\left(x^{2}+8\right)^{2}}\)
Equate first derivative to zero and attempt solution to get \(x=\ldots\)
Obtain \(2 \pm \sqrt{12}\) or exact equivalents
\(\operatorname{Obtain} \frac{\left(x^{2}+8\right)-2 x(x-2)}{\left(x^{2}+8\right)^{2}}\)
Equate first derivative to zero and attempt solution to get \(x=\ldots\)
Obtain \(2 \pm \sqrt{12}\) or exact equivalents
Knowledge points:
2.4.2 differentiate products and quotients
Solution:
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