Applications of Differentiation

2019 ASRJC Promo Q3 A curve $C$ has equation ${{left( ln y right)}^{2}}-3xy+{{x}^{2}}-4=0$. (i) Show that $frac{text{d}y}{text{d}x}=frac{left( 3y-2x right)y}{2ln y-3xy}$. [3] (ii) It is given that $C$ contains the point

2019 EJC Promo Q3 The curve $C$ has equation ${{a}^{2}}{{x}^{2}}-{{y}^{2}}-2left( ax-2y+2 right)=0$ where $a$ is a constant such $ain mathbb{R}backslash left{ 0 right}$. Show that $frac{text{d}y}{text{d}x}=frac{aleft( ax-1 right)}{y-2}$. Hence, find

2021 RI Promo Q2 The curve $C$ has equation ${{y}^{3}}=4-frac{x{{y}^{2}}}{2}$. (i) Show that $frac{text{d}y}{text{d}x}=-frac{y}{6y+2x}$. [2] (ii) Find the equation of the normal to $C$ at the point $P$ where $y=1$.

2019 RI Promo Q1 Find the equation of the tangent to the curve ${{y}^{3}}-2x{{y}^{2}}+3{{x}^{2}}-3=0$ at the point $left( 2,3 right)$. [3] Suggested Video and handwritten Solutions Written by Did You Enjoy

2018 NJC Promo Q12 (a) The diagram below (not drawn to scale) shows a cross-section of an empty swimming pool measuring $50$m long, $20$m wide and $2$ m deep. Suppose

2021 TJC Promo Q4 In the figure (not drawn to scale), $POQ$ is a rail and $angle POQ=frac{pi }{6}$. $AB$ is a rod of fixed length $1$ m which is

2021 EJC Promo Q9 (b) Fig. 2 shows a $2.6$ m long pole sliding down along a vertical wall such that the top of the pole is slipping at the

Home 2009 ACJC P1 Q7 A point $left( x,y right)$ lies on the curve with equation $frac{1}{x}+frac{1}{y}=frac{1}{a}$, where $a$ is a non-zero constant, $xne 0$ and $yne 0$. (i) Express