The function $f(x) = x^4 - 4x^3 + 6$ is defined for all real numbers. Describe the key features of the graph of $y = f(x)$, including the coordinates and nature of any stationary points, the intervals where the function is strictly increasing or strictly decreasing, and any points of inflection. Fully justify your answer with appropriate calculus techniques.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 7 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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