The curve has the equation $x+y={{\left( x-y \right)}^{2}}$. It is given that $C$ has only one turni

Question

The curve has the equation $x+y={{\left( x-y \right)}^{2}}$. It is given that $C$ has only one turning point. Show that $1-\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{2}{1+2x-2y}$. [4] Hence, or otherwise, show that $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}={{\left( 1-\frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{3}}$. [3] Hence state, with a reason, whether the turning point is a minimum or a maximum. [2]

Accepted Answer

$$\dfrac{d^2y}{dx^2} = \left(1 - \dfrac{dy}{dx}\right)^3$$

2023 EJC Promo Q8

2023 EJC Promo Q8

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