IB Maths AA HL Sl 5 3 Derivative of Powers Questions

Practise differentiating integer powers and sums of power terms, identifying the correct derivative rule and checking the resulting function or rate of change.

Exam points

Differentiate power and polynomial functions, including negative or fractional powers, and evaluate the derivative at a specified input.
Use first and higher derivatives to find gradients, rates of change and the derivative of a derivative in algebraic or function-graph contexts.
Use a derivative condition such as a specified gradient, stationary point or point of inflexion to determine an unknown parameter.
Prove or verify derivative relationships for polynomial functions by connecting secant gradients with endpoint derivatives.

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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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Consider the function $f(x)=a x^{3}+b x^{2}+c x+d$ , where $x \in \mathbb{R}$ and $a, b, c, d \in \mathbb{R}$ .

Write down an expression for $f^{\prime}(x)$ .

$f^{\prime}(x)=3 a x^{2}+2 b x+c \quad \boldsymbol{A} \mathbf{1}$

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