IB Maths AI HL 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: 5]

Linda owns a field, represented by the shaded region R. The plan view of the field is shown in the following diagram, where both axes represent distance and are measured in metres.

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

The segments [AB], [CD] and [AD] respectively represent the western, eastern and southern boundaries of the field. The function, f(x), models the northern boundary of the field between points B and C and is given by

f(x)=\frac{-x^{2}}{50}+2 x+30, \text { for } 0 \leq x \leq 70

Find $f^{\prime}(x)$ .

$f^{\prime}(x)=\frac{-2 x}{50}+2\left(=\frac{-x}{25}+2,-0.04 x+2\right) \quad$ A1A1

Note: Award A1 for each correct term. Award at most A0A1 if extra terms are seen.

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SL 5.3—Derivative of powers question 1