<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Given that&nbsp;\(y = x^3 - x\), find the range of values of \(x\) such that&nbsp;\(x \frac{\mathrm{d}^2 y}{\mathrm{d}x^2} + \frac{\mathrm{d}y}{\mathrm{d}x} &gt; 0\).<span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">A curve is such that&nbsp;\(\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{1}{3\sqrt{2x - 1}}\). Given that the curve has a gradient of \(3\) at the point \((1, 6)\), find the equation of the curve.<span class="inline-marks">[4]</span></div></li></ol>

Given that \(y = x^3 - x\), find the range of values of \(x\) such that \(x \frac{\mathrm{d}^2 y}{\mathrm{d}x^2} + \frac{\mathrm{d}y}{\mathrm{d}x} > 0\).

A curve is such that \(\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{1}{3\sqrt{2x - 1}}\). Given that the curve has a gradient of \(3\) at the point \((1, 6)\), find the equation of the curve.

Applications of Integration

Applications of Integration