Can some one please tell me what f'(a) times deltaX means? Does it represent a length, a slope, or an area? What about f(a) times deltaX?
Thanks to anyone who can help me with these questions!
f'(a) is the slope of the function at x=a.
f'(a)*deltaX can be understood to be the displacement of the function given the small displacement of x.
f(a) is the value of the function at x = a.
f(a)*deltaX can be understood to be, with a measurable error, the area under the curve - a tiny rectangle with base deltaX and height f(a).
It is when deltaX shinks that things get REALLY interesting.