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3.5.2 Differentiation (A-level only)

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Question 67

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 $dNdt\frac{dN}{dt}$ .

[3]

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 $P$ .

[4]

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

[2]

Markscheme

3.5.2 Differentiation (A-level only) Questions

A Level
Maths
3.5.2 Differentiation (A-level only)

109 exam-style questions on CCEA A Level Maths 3.5.2 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

3.5.2 Differentiation (A-level only)

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3.5.2 Differentiation (A-level only)

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Question 67

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 $dNdt\frac{dN}{dt}$ .

[3]

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 $P$ .

[4]

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

[2]

Markscheme

3.5.2 Differentiation (A-level only) Questions

A Level
Maths
3.5.2 Differentiation (A-level only)

109 exam-style questions on CCEA A Level Maths 3.5.2 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.