The website below provides a nice, clear and straightforward discussion on the difference between average slope and the first derivative. I have attempted to summarize some of the key points.
https://www0.gsb.columbia.edu/premba/analytical/s4/s4_4.cfm
Finding slope of a curve
1. Draw a line through two points on the curve which are very close to the selected point and then measure the slope of the line drawn. The closer the two points are together, the closer the the slope of the secant line is to the actual slope of the curve at the point of interest.
2. Draw a line tangential to the point of interest on the curve. The tangent line's slope is called the "instantaneous rate of change" because it is a precise measurement of the slope of the curve at that particular point. Use the first derivative of the nonlinear function to find the slope of the tangent line at any point on the curve without having to find the equation of the tangent line.
The derivatives of some commonly encountered quantities are:
http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/BASICMAT/node5.html
Finding Minimum and Maximum
The maximum and minimum points can be found by taking the first derivative of the function, setting it equal to zero, and solving for x.
No comments:
Post a Comment