Rates of change and the concept of derivatives
Mathematical Methods · Unit 2 — Calculus and further functions · Introduction to differential calculus
Learning objectives (7)
LO-1Calculate derivatives of power and polynomial functions. Mathematical Methods 2025 v1.3LO-2Determine average rate of change in a variety of practical contexts.LO-3Interpret the derivative as the gradient of a tangent line of the graph of 𝑦 = 𝑓(𝑥).LO-4Interpret the derivative as the instantaneous rate of change.LO-5Understand the concept of the derivative as a function.LO-6Use the rule 𝑑 𝑑𝑥 𝑥𝑛 = 𝑛𝑥𝑛−1 for positive integers.LO-7Use the rule 𝑓′(𝑥) = lim ℎ→0 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ to determine the derivative of simple power functions and polynomial functions from first principles.
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