Stationary points and classification

Practise stationary points and classification with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=x^3-3x^2+2$. (a) Find the coordinates of every stationary point. [2 marks] (b) Classify both stationary points. [2 marks]

Worked explanation

• Part (a)

  $f\prime(x)=3x(x-2)=0$ gives $x=0,2$. Substituting into f gives 2 and $-2$.

• Part (b)

  $f\prime\prime(x)=6x-6$. At 0 it is negative, so there is a local maximum; at 2 it is positive, so there is a local minimum.

(a) $(0,2)$ and $(2,-2)$.; (b) Local maximum at $(0,2)$; local minimum at $(2,-2)$.

Original VectorPaths practice; not an official VCAA question or marking rubric.