A curve has equation $$\(y=\mathrm{f}(x)\)$$, and it is given that $$\(\mathrm{f}^{\prime}(x)=2 x^{2}-7-\frac{4}{x^{2}}\)$$. Given that $$\(\mathrm{f}(1)=-\frac{1}{3}\)$$, find $$\(\mathrm{f}(x)\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_11 Year：2021 Question No：9(a)
Answer:
\(
f(x)=\frac{2}{3} x^{3}-7 x+4 x^{-1} \quad[+c]
\)
\(-\frac{1}{3}=\frac{2}{3}-7+4+c \quad\) leading to \(c=[2]\)
\(
f(x)=\frac{2}{3} x^{3}-7 x+4 x^{-1}+2
\)
f(x)=\frac{2}{3} x^{3}-7 x+4 x^{-1} \quad[+c]
\)
\(-\frac{1}{3}=\frac{2}{3}-7+4+c \quad\) leading to \(c=[2]\)
\(
f(x)=\frac{2}{3} x^{3}-7 x+4 x^{-1}+2
\)
Knowledge points:
1.8.1 understand integration as the reverse process of differentiation, and integrate (for any rational n except-1 , together with constant multiples, sums and differences
1.8.2 solve problems involving the evaluation of a constant of integration
Solution:
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