<p>A curve has equation \(y=x^n\sqrt{a^2-x^2}\), where&nbsp;\(a\) and \(n\) are integer constants such that&nbsp;\(a \ge 2\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\) in terms of \(x\), \(a\) and \(n\), expressing your answer as a single fraction in a fully factorised form.</span><span class="inline-marks">[4]</span></div></li></ol>
<p>It is given that the curve has the same gradient value at both&nbsp;\(x=1\) and \(x=-1\).</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find a condition that&nbsp;\(n\) must satisfy.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that the curve has a gradient of \(0\) at \(x=\sqrt{2}\), find the values of \(a\) and \(n\). Justify your answers clearly.</span><span class="inline-marks">[4]</span></div></li></ol>

A curve has equation \(y=x^n\sqrt{a^2-x^2}\), where \(a\) and \(n\) are integer constants such that \(a \ge 2\).

Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\) in terms of \(x\), \(a\) and \(n\), expressing your answer as a single fraction in a fully factorised form.

It is given that the curve has the same gradient value at both \(x=1\) and \(x=-1\).

Find a condition that \(n\) must satisfy.

Given that the curve has a gradient of \(0\) at \(x=\sqrt{2}\), find the values of \(a\) and \(n\). Justify your answers clearly.

NJC IP4 Techniques of Differentiation Tutorial Q3

NJC IP4 Techniques of Differentiation Tutorial Q3

Video Solution:

Solution:

Handwritten Solution