A biologist is studying the population of a particular species of insect in a controlled environment. The population, $P(t)$, at time $t$ (in weeks) is modelled by the function $$P(t) = rac{1}{4}t^4 - t^3 + rac{5}{2}t^2 + 100$$, where $t \ge 0$.
a. Determine the intervals of time when the insect population is increasing and decreasing.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Differentiation for Graph Sketching. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
application of differentiation to graph sketching and identification of key features of graphs, including stationary points and points of inflection, and intervals over which a function is strictly increasing or strictly decreasing
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