3.22: Product rule, no stationary points, and rates

Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{35x^{2} + 15x + 1}{(2x + 1)^{\frac{2}{3}}}$.

Show that there are no stationary points on this curve.

Find the approximate change in $y$ when $x$ increases from $1$ to $1 + p$, where $p$ is small.

Given that when $x = 1$ the rate of change in $x$ is $2.5$ units per second, find the corresponding rate of change in $y$.