Expanding, splitting and increasing or decreasing Problem set B Answers

1. (a) \(\frac{dy}{dx}=3p - \frac{12q}{x^{4}}\)
2. (b) \(\frac{dy}{dx}=14q^{2}x + \frac{8p}{rx^{2}}\)

1. (a) \(\frac{dy}{dx}=2k^{2}x\)
2. (b) \(\frac{dy}{dx}=50p^{2}x\)

1. (a) \(\frac{dy}{dx}=2x + k + r\)
2. (b) \(\frac{dy}{dx}=2krx + k^{2} + r^{2}\)

1. (a) \(\frac{dy}{dx}=\frac{9}{x^{2}}\)
2. (b) \(\frac{dy}{dx}=-\frac{5}{x^{2}} - \frac{4}{x^{3}}\)
3. (c) \(\frac{dy}{dx}=6x^{2} + \frac{2}{3}x\)

1. (a) \(x<3\)
2. (b) \(x>4\)

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

\(\frac{dw}{dp}=7 - \frac{10}{p^{2}}\)

\(\frac{dy}{dx}=2x - 4\)

1. (a) \(\frac{dU}{dT}=\frac{5nR}{2}\)
2. (b) 62.3 joules per kelvin

1. (a) \(\frac{dN}{dd}=-\frac{k}{d^2}\)
2. (b) \(-\frac{N^2}{k}\)
3. (c) 9

1. (a) \(\frac{dD}{dt}=p+6pt=p(1+6t)\)
2. (b) The distance walked cannot fall, so \(\frac{dD}{dt}>0\). That needs p > 0.

\(f'(x)=6x^2+9>0\) for all x

1. (a) \(f'(x)=\frac{1}{3} - \frac{k}{3x^{2}}\)
2. (b) k = 6