Chapter 2: Differentiation Test Review
To review for Test 2:
- Read the following list of skills you need to be able to demonstrate.
- Go over all homework and do the chapter review. Many of the
test questions will look very similar to some problem in the homework.
- Remember that this test will also include some problems from
Chapter 1. Be sure that you fully understand everything on that
test and the assigned problems in the Chapter Review.
List of Topics:
- Velocity as related to distance. Average velocity and instantaneous
velocity.
- Rate of change of a function. Average rate of change and instantaneous
rate of change. The derivative at a point as the instantaneous
rate of change. Graphical interpretation of each (slope of a line
between two points and slope of the tangent line).
- Estimating the derivative at a point graphically, numerically,
and finding it algebraically (as long as the algebra doesn't get
too hard!). Also, understanding which is which, so that you can
do each problem by the method requested.
- Generalizing to the derivative function. Graphing a derivative
function from a graph of the function. The derivative and how
it relates to whether the function is increasing or decreasing.
- Interpretation of the derivative as a rate of change. Keeping
track of the units. Acceleration. Different types of notation
for the derivative.
- The second derivative as the rate of change of the first derivative.
Concavity.
- Writing the equation of the tangent line to the graph at a
point (which involves finding the value of the derivative. Recall
number 3 here!). Using that tangent line to estimate a function
value. Is this an overestimate or underestimate?
- For a given function (graph), tell where it is continuous
or not and where it is differentiable or not. Use limit notation
and one-sided limit notation.
Chapter 2 Review: (These won't be graded, but you may find them
useful.)
1, 2, all of 8-14 (and compare your answers with those of other
students), 15, 16, 17, 18, 19 (you don't have to graph it all
that carefully to get an estimate of the slope that is accurate
enough for this problem), 21
Last updated December 23, 1997. mparker@austincc.edu