The gradient of a curve at the point $$\((x, y)\)$$ is given by $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=2(x+3)^{\frac{1}{2}}-x\)$$. The curve has a stationary point at $$\((a, 14)\)$$, where $$\(a\)$$ is a positive constant. Find the equation of the curve. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：10(c)
Answer:
\((y=) \frac{2(x+3)^{\frac{3}{2}}}{\frac{3}{2}}-\frac{1}{2} x^{2}(+c)\)
Sub \(x=\) their \(a\) and \(y=14 \rightarrow 14=\frac{4}{3}(9)^{\frac{3}{2}}-18+c\)
\(y=\frac{4}{3}(x+3)^{\frac{3}{2}}-\frac{1}{2} x^{2}-4\)
Sub \(x=\) their \(a\) and \(y=14 \rightarrow 14=\frac{4}{3}(9)^{\frac{3}{2}}-18+c\)
\(y=\frac{4}{3}(x+3)^{\frac{3}{2}}-\frac{1}{2} x^{2}-4\)
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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