Sketch curves associated with power functions and polynomials up to degree 4; find stationary points and local and global maxima and minima with and without technology; and examine behaviour as 𝑥 → ∞ and 𝑥 → − ∞.

Consider the function $f(x) = 2x^3 - 9x^2 + 12x - 4$. (a) Find the coordinates of the stationary points of $f(x)$ and classify each as a local maximum or local minimum. [2 marks] (b) State the behaviour of $f(x)$ as $x \to \infty$ and as $x \to -\infty$. [1 mark]

Consider the polynomial function \( f(x) = -x^4 + 8x^2 - 7 \). (a) Determine the coordinates of all stationary points of \( f(x) \), showing all algebraic working. (2 marks) (b) Classify each stationary point as a local maximum or local minimum, justifying your answer. (1 mark) (c) State the behaviour of the function as \( x \to \infty \) and as \( x \to -\infty \). (1 mark)

Determine the coordinates of the stationary points of the function \( f(x) = x^3 - 6x^2 + 9x + 2 \).

The graph below shows a polynomial function \( f(x) \) of degree 4. Which statement correctly describes the behaviour and features of \( f(x) \)?