Why are the turning points of a cubic graph called local maximum and local minimum points?

1. A cubic graph rises, turns, falls, turns again and then rises without limit. 2. At each turning point the gradient is zero, so the tangent there is horizontal. 3. But the arms of the graph carry on past those turns to higher and lower values. 4. So each turning point is only the highest or lowest value in its own neighbourhood, which is what local means. 5. A cubic graph has no axis of symmetry through its turning points, so that option is wrong. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_