A curve has equation $$\(y=\mathrm{f}(x)\)$$ where $$\(\mathrm{f}(x)=\frac{4 x^{3}+8 x-4}{2 x-1}\)$$. Find an expression for $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ and hence find the coordinates of each of the stationary points of the curve $$\(y=f(x)\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_21 Year：2020 Question No：8(a)
Answer:
Differentiate using the quotient rule (or product rule)
Obtain \(\frac{(2 x-1)\left(12 x^{2}+8\right)-2\left(4 x^{3}+8 x-4\right)}{(2 x-1)^{2}}\)
Equate first derivative to zero and attempt solution
Obtain \((0,4)\)
\(\operatorname{Obtain}\left(\frac{3}{4}, \frac{59}{8}\right)\)
Obtain \(\frac{(2 x-1)\left(12 x^{2}+8\right)-2\left(4 x^{3}+8 x-4\right)}{(2 x-1)^{2}}\)
Equate first derivative to zero and attempt solution
Obtain \((0,4)\)
\(\operatorname{Obtain}\left(\frac{3}{4}, \frac{59}{8}\right)\)
Knowledge points:
2.1.3 use the factor theorem and the remainder theorem.
2.4.2 differentiate products and quotients
Solution:
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