Expanding, splitting and increasing or decreasing Problem set A Answers

1. (a) \(\frac{dy}{dx}=8a + \frac{10b}{x^{3}}\)
2. (b) \(\frac{dy}{dx}=12b^{2}x^{2} - \frac{6a}{cx^{2}}\)

1. (a) \(\frac{dy}{dx}=2b^{2}x\)
2. (b) \(\frac{dy}{dx}=32a^{2}x\)

1. (a) \(\frac{dy}{dx}=2x + p + q\)
2. (b) \(\frac{dy}{dx}=2pqx + p^{2} + q^{2}\)

1. (a) \(\frac{dy}{dx}=-\frac{12}{x^{2}}\)
2. (b) \(\frac{dy}{dx}=\frac{1}{x^{2}} - \frac{6}{x^{3}}\)
3. (c) \(\frac{dy}{dx}=4x + \frac{1}{2}\)

1. (a) \(x<2\)
2. (b) \(x>5\)

1. (a) \(x>3\)
2. (b) \(x>-\frac{b}{2}\)

\(\frac{ds}{dt}=8 + \frac{9}{t^{2}}\)

\(\frac{dy}{dx}=10x - 3\)

1. (a) \(\frac{dH}{dT}=cm\)
2. (b) 2.25 joules per °C

1. (a) \(\frac{d\theta}{dd}=-\frac{k}{d^2}\)
2. (b) \(-\frac{\theta^2}{k}\)
3. (c) 4

1. (a) \(\frac{dH}{dd}=q+4qd\)
2. (b) A plant does not get shorter, so \(\frac{dH}{dd}>0\). That needs q > 0.

\(f'(x)=9x^2+4>0\) for all x

1. (a) \(f'(x)=\frac{1}{2} - \frac{k}{2x^{2}}\)
2. (b) k = 2