On the top of the hill, it is flat. Only momentarily flat, sure, but nevertheless flat. It’s a point where the curvature changes from upwards-pointing to downwards-pointing. At that point you are neither walking upwards nor downwards.
That’s of course also the case in the bottom of a valley or lake where the curvature changes from downwards-pointing to upwards-pointing.
- ‘Turning Points and Nature’ (web page), The Mathematics Capital: iitutor, 2019, www.iitutor.com/turning-points-and-nature/ (accessed Jun. 20th, 2020)
- ‘Stationary Points’ (web page), Best Maths Online, 2014, www.bestmaths.net/online/index.php/year-levels/year-12/year-12-topic-list/stationary-and-turning-points (accessed Jun. 20th, 2020)
- ‘Stationary Points’ (web page), Newcastle University, ASK Academic Skills Kit, 2018, internal.ncl.ac.uk/ask/numeracy-maths-statistics/core-mathematics/calculus/stationary-points.html (accessed Jun. 20th, 2020)
- ‘Uses of Differentiation’ (web page), Revision Maths, 2004 www.revisionmaths.com/advanced-level-maths-revision/pure-maths/calculus/uses-differentiation (accessed Jun. 20th, 2020)
- ‘The first derivative and stationary points’ (article), Jackie Nicholas, The University of Sydney, Mahtematics Learning Centre, 2004, www.sydney.edu.au/content/dam/students/documents/mathematics-learning-centre/first-derivative-and-stationary-points.pdf (accessed Jun. 20th, 2020)