IB Maths AI SL 5.3 Derivative of Powers Questions

Practise differentiating ax^n and sums of integer powers, evaluating the derivative as a gradient or rate, and checking domain, units and context.

Exam points

Differentiate ax^n and sums of integer-power terms using the power rule.
Evaluate a derivative at a point or use it as a gradient/rate of change.
Check the resulting expression, domain and units in the applied context.

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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 $x \mathrm{~cm}$ .

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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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IB Maths AI SL 5.3 Derivative of Powers Questions question 1