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!

-M

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- November 2nd 2007, 09:22 AMblurainHomework Help
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!

-M - November 2nd 2007, 02:09 PMTKHunny
deltaX is a small displacement along the x-axis.

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.