The population $N$ of a specific bacteria culture, in thousands, is modeled by the equation

\frac{(2t+2)^2}{8} + 12\sqrt[3]{2t+2}

for $\ge 0$ , where $t$ is the time in hours since the start of an experiment.

Find an expression for $dNdt\frac{dN}{dt}$ .

The point $P$ with coordinates $(3, 32)$ lies on the graph of the population model. Find an equation of the tangent to the curve at the point $P$ .

Show that the model predicts no stationary points for the population for $\ge 0$ .

The population $N$ of a specific bacteria culture, in thousands, is modeled by the equation

\frac{(2t+2)^2}{8} + 12\sqrt[3]{2t+2}

for $\ge 0$ , where $t$ is the time in hours since the start of an experiment.

Find an expression for $dNdt\frac{dN}{dt}$ .

The point $P$ with coordinates $(3, 32)$ lies on the graph of the population model. Find an equation of the tangent to the curve at the point $P$ .

Show that the model predicts no stationary points for the population for $\ge 0$ .

3.6.5 Differentiation (A-level only)

3.6.5 Differentiation (A-level only) Questions