Find the turning points of the curve
\(y=4x^3+x^2-1\).
\(\begin{aligned} &(0,-1) \\\\ &\text{and}\\\\ &\begin{pmatrix} -\dfrac{1}{6},-\dfrac{87}{108} \end{pmatrix} \end{aligned}\)
Find the minimum point of the curve
\(\begin{pmatrix} -\dfrac{1}{6},-\dfrac{107}{108} \end{pmatrix}\)
Given that
\(f(x)=\dfrac{1}{(10x-k)^2}\),
where \(k\) is a constant, find the value of \(k\) if
\(f'(1)=20\).
\(12\)
A closed cylinder has a height of \(15 \text{ cm}\).
Find the approximate increase in the total surface area of the cylinder when the radius of the cylinder increases from \(5 \text{ cm}\) to \(5.01 \text{ cm}\) while its height is a constant.
\(\begin{aligned} 0.4 \pi \text{ cm}^2 \end{aligned}\)
\(PQRS\) is a rectangle with \(5x \text{ cm}\) length and \((4-x) \text{ cm}\) width.
Find the perimter, in \(\text{cm}\), of \(PQRS\) if the area of \(PQRS\) is maximum.
\(34 \text{ cm}\)
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