IB Maths AI HL 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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Study SL 5.3—Derivative of powers conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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 IB Maths AI HL Sl 5 3 Derivative of Powers Questions 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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IB Maths AI HL Sl 5 3 Derivative of Powers Questions question 1