Math: Nature Knows Calculus

I'm attempting to have a better understanding of practical mathematics from the NY Times article by Steven Strogatz. Here's my attempt at Calculus, the mathematics of change. The derivative tells you how fast something is changing.

Many times the derivative is displayed in graphical form as a slope. A general principle can by shown that change is slowest, or the most sluggish at its extremes (where the derivative is zero).

The example given, is Michael Jordan dunking a basketball. When he initially leaves the ground, his rate of elevation is changing rapidly. However, as he reaches the peak of his jump, the rate comes to a halt, the derivative is zero, or he is momentarily hanging.

He naturally expresses differential calculus without knowing. The article gives many other examples (they are everywhere) with much better explanation. I still feel lost, but take comfort in the observation of nature practicing the same basic principles.