stationary points

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

3 practice marks

Original practice question

For $h(x) = 1x^3 + 0x^2 + -6x + 0$, find all turning points and classify them.

Worked explanation

• Find f'(x)

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

• Find stationary points

  \[x = - \sqrt{2}, \sqrt{2}\]

• Use second derivative test

  \[(- \sqrt{2}, 4 \sqrt{2}) \text{ is a local maximum}; \quad (\sqrt{2}, - 4 \sqrt{2}) \text{ is a local minimum}\]

\[(- \sqrt{2}, 4 \sqrt{2}) \text{ is a local maximum}; (\sqrt{2}, - 4 \sqrt{2}) \text{ is a local minimum}\]

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