The function $f(x) = rac{ax^3}{x^2 + b}$, where $a$ and $b$ are non-zero real numbers, has a stationary point at $(1, 1)$. Analyse the conditions on $a$ and $b$, and hence determine the nature of the stationary point at $x=1$. Justify your answer with appropriate calculus.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 6 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
All free, all instant AI marking.
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 co…
The function $f(x) = x^3 - 3x^2$ is defined for all real numbers. Identify the $x$-coordinate(s) of any stationary point(s) of the function…
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Differentiation for Graph Sketching.
