Applications of Differentiation

2023 NYJC P1 Q8 The curve $C$ is a circle with equation ${{x}^{2}}+{{y}^{2}}-8x-6y-20=0$. (a) $C$ crosses the positive $x$-axis at point $A$. Find the equation of ${{l}_{1}}$, the tangent to

2023 RI P1 Q11 One geometric optimization problem concerns finding the largest area axis-parallel rectangle inside an object.The largest area rectangle problem has many industrial applications. For example, consider a

2022 RI Promo Q11 [It is given that a right circular cone of radius $r$ and height $h$ has total surface area $pi {{r}^{2}}+pi rsqrt{{{r}^{2}}+{{h}^{2}}}$ and volume $frac{1}{3}pi {{r}^{2}}h$.]An ice-cream

2022 HCI Promo Q2 The equation of a curve $G$ is given by ${{x}^{2}}y-ln y=1$, where $x<0$ and $y>0$. (a) Show that $frac{text{d}y}{text{d}x}=frac{2x{{y}^{2}}}{1-{{x}^{2}}y}$. [3] (b) Find the equation of the

2022 DHS Promo Q5 A curve $C$ has equation $frac{1-{{x}^{2}}{{y}^{2}}}{3{{y}^{2}}+{{x}^{2}}}=frac{1}{2}$. (a) Show that $frac{text{d}y}{text{d}x}=frac{-x-2x{{y}^{2}}}{yleft( 3+2{{x}^{2}} right)}$. [3] (b) Find the equations of the tangents to the curve that are parallel

2021 ASRJC Promo Q4 A curve $C$ has equation ${{y}^{3}}-2x{{y}^{2}}+3{{x}^{2}}-3=0$ (i) Find $frac{text{d}y}{text{d}x}$ in terms of $x$ and $y$. [2] (ii) Find the equation of the normal to the curve

2018 CJC Promo Q10 (b) During the performance, a drone is positioned at the center of the circular stage, $O$, and a performer is standing at the circumference of the