stationary points

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

3 practice marks

Original practice question

Find the stationary points of $g(x) = 1x^3 + -3x^2 + -6x + -1$ and determine their nature.

Worked explanation

• Find f'(x)

  \[f'(x) = 3 x^{2} - 6 x - 6\]

• Find stationary points

  \[x = 1 - \sqrt{3}, 1 + \sqrt{3}\]

• Use second derivative test

  \[(1 - \sqrt{3}, -9 + 6 \sqrt{3}) \text{ is a local maximum}; \quad (1 + \sqrt{3}, - 6 \sqrt{3} - 9) \text{ is a local minimum}\]

\[(1 - \sqrt{3}, -9 + 6 \sqrt{3}) \text{ is a local maximum}; (1 + \sqrt{3}, - 6 \sqrt{3} - 9) \text{ is a local minimum}\]

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