IB Maths AI SL 5.3 Derivative of powers Question Bank

Practise IB Mathematics SL/HL 5.3 by applying derivative of powers methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 2]

A hollow chocolate box is manufactured in the form of a right prism with a regular hexagonal base. The height of the prism is $h \mathrm{~cm}$ , and the top and base of the prism have sides of length $x \mathrm{~cm}$ .

Figure for Question SL 5.3—Derivative of powers question 1 — IB Maths AI SL

Find an expression for $\frac{\mathrm{d} V}{\mathrm{~d} x}$ .

$\frac{\mathrm{d} V}{\mathrm{~d} x}=300 \sqrt{3}-\frac{27}{4} x^{2}$

Note: Award A1 for a correct term.

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SL 5.3—Derivative of powers question 1