The population NNN of a specific bacteria culture, in thousands, is modeled by the equation
N(t)=(2t+2)28+122t+23 N(t) = \frac{(2t+2)^2}{8} + 12\sqrt[3]{2t+2} N(t)=8(2t+2)2+1232t+2for t≥0t \ge 0t≥0, where ttt is the time in hours since the start of an experiment.
Find an expression for dNdt\frac{dN}{dt}dtdN.
The point PPP with coordinates (3,32)(3, 32)(3,32) lies on the graph of the population model. Find an equation of the tangent to the curve at the point PPP.
Show that the model predicts no stationary points for the population for t≥0t \ge 0t≥0.
50 exam-style questions on OCR (MEI) A Level Maths 1.9.14 Chain rule (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.