<p>A curve has equation \(y = \frac{x^{n+1}}{n+1} + \frac{a}{x}\) for some non-zero constants \(a\) and \(n\). The curve has a common gradient value of \(\frac{5}{2}\) at both&nbsp;\(x = \sqrt{2}\) and \(x = \frac{1}{\sqrt{2}}\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">By using the substitution \(b = 2^{\frac{n}{2}}\), find the equation of the curve.</span><span class="inline-marks">[7]</span></div></li><li><div class="list-item-content"><span class="list-item-text">By considering the expansion of \(\left( x - \frac{1}{x} \right)^2\), show that the gradient of the curve at all points on the curve is at least \(2\).</span><span class="inline-marks">[3]</span></div></li></ol>

A curve has equation \(y = \frac{x^{n+1}}{n+1} + \frac{a}{x}\) for some non-zero constants \(a\) and \(n\). The curve has a common gradient value of \(\frac{5}{2}\) at both \(x = \sqrt{2}\) and \(x = \frac{1}{\sqrt{2}}\).

By using the substitution \(b = 2^{\frac{n}{2}}\), find the equation of the curve.

By considering the expansion of \(\left( x - \frac{1}{x} \right)^2\), show that the gradient of the curve at all points on the curve is at least \(2\).

NJC IP4 Techniques of Differentiation Tutorial Q1

NJC IP4 Techniques of Differentiation Tutorial Q1

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