<p>Let&nbsp;\(f(x) = \sin^3{x}\).</p>
<ol class="abc-list"><li><ol class="i-list"><li><div class="list-item-paragraph">Write down the range of the function \(f\).</div></li><li><div class="list-item-paragraph">Consider \(f(x) -1, 0 \leq x \leq 2\pi\). Wirte down the number of solutions to this equation. <br>Justify your answer.</div></li></ol></li><li><div class="list-item-paragraph">Find \(f'(x)\), giving your answer in the form \(a\sin^p{x} \cos^1{x}\) where&nbsp;\(a, p, q, \in \mathbb{Z}\).</div></li><li><div class="list-item-paragraph">Let&nbsp;\(g(x) = \sqrt{3} \sin{x} (\cos{x})^{\frac{1}{2}}\) for&nbsp;\(0 \leq x \leq \frac{\pi}{2}\). Find the volume generated when the curve of \(g\) is revolved through \(2\pi\) about the \(x\)-axis.</div></li></ol>

Find \(f'(x)\), giving your answer in the form \(a\sin^p{x} \cos^1{x}\) where \(a, p, q, \in \mathbb{Z}\).

Let \(g(x) = \sqrt{3} \sin{x} (\cos{x})^{\frac{1}{2}}\) for \(0 \leq x \leq \frac{\pi}{2}\). Find the volume generated when the curve of \(g\) is revolved through \(2\pi\) about the \(x\)-axis.

Derivatives of Exponential, Logarithmic and Trigonometric Functions

International Baccalaureate Standard Level Mathematics