The point $$\((4,7)\)$$ lies on the curve $$\(y=\mathrm{f}(x)\)$$ and it is given that $$\(\mathrm{f}^{\prime}(x)=6 x^{-\frac{1}{2}}-4 x^{-\frac{3}{2}}\)$$. Find the equation of the curve. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：7(b)
Answer:
\(\frac{6 x^{\frac{1}{2}}}{\frac{1}{2}}-\frac{4 x^{-\frac{1}{2}}}{-\frac{1}{2}}(+c)\)
Uses \((4,7)\) leading to \(c=(-21)\)
\(y\) or \(f(x)=12 x^{\frac{1}{2}}+8 x^{-\frac{1}{2}}-21\) or \(12 \sqrt{x}+\frac{8}{\sqrt{x}}-21\)
Uses \((4,7)\) leading to \(c=(-21)\)
\(y\) or \(f(x)=12 x^{\frac{1}{2}}+8 x^{-\frac{1}{2}}-21\) or \(12 \sqrt{x}+\frac{8}{\sqrt{x}}-21\)
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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