CHAPTER SUMMARY
In this chapter we reviewed many applications of derivatives. We’ve
seen how to find slopes of curves and used that skill to write equations
of lines tangent to a curve. Those lines often provide very good
approximations for values of functions. We have looked at ways
derivatives can help us understand the behavior of a function. The first
derivative can tell us whether a function is increasing or decreasing and
locate maximum and minimum points. The second derivative can tell us
whether the graph of the function is concave upward or concave
downward and locate points of inflection. We’ve reviewed how to use
derivatives to determine the velocity and acceleration of an object in
motion along a line and to describe relationships among rates of change.
For BC Calculus students, this chapter reviewed finding slopes of
curves defined parametrically or in polar form. We have also reviewed
the use of vectors to describe the position, velocity, and acceleration of
objects in motion along curves.