The gradient of a curve at the point $$\((x, y)\)$$ is given by $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=2(x+3)^{\frac{1}{2}}-x\)$$. The curve has a stationary point at $$\((a, 14)\)$$, where $$\(a\)$$ is a positive constant. Find the value of $$\(a\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：10(a)
Answer:
\(2(a+3)^{\frac{1}{2}}-a=0\)
\(4(a+3)=a^{2} \rightarrow a^{2}-4 a-12=0\)
\((a-6)(a+2) \rightarrow a=6\)
\(4(a+3)=a^{2} \rightarrow a^{2}-4 a-12=0\)
\((a-6)(a+2) \rightarrow a=6\)
Knowledge points:
1.1.5 recognise and solve equations in which are quadratic in some function of
1.7.4 locate stationary points and determine their nature, and use information about stationary points in sketching graphs. (Including use of the second derivative for identifying maxima and minima; alternatives may be used in questions where no method is specified.) (Knowledge of points of inflexion is not included.)
Solution:
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