<p>A curve \(C\) has equation \(x^2 y^2 + 3xy + 2y^2 - x - 2 = 0\).</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\) in terms of \(x\) and \(y\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the gradients of the tangents at \(x = 0\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Using an algebraic method, show that there is no part of the curve for which \(x &lt; -4\).<span class="inline-marks">[3]</span></div></li></ol>

A curve \(C\) has equation \(x^2 y^2 + 3xy + 2y^2 - x - 2 = 0\).

Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\) in terms of \(x\) and \(y\).

Find the gradients of the tangents at \(x = 0\).

Using an algebraic method, show that there is no part of the curve for which \(x < -4\).

Applications of Differentiation

International Baccalaureate Higher Level Mathematics

2024 NJC Promo Q6

2024 NJC Promo Q6