CHAPTER 3 SECTION 1 - 6

Some Highlights:

a) To find the intervals where a function is increasing or decreasing, find where f ' is either equal to zero, or undefined. This gives you the critical numbers. Test values of x between each critical number in the first derivative. If f ' is positive there, the function is increasing. If f ' is negative there, the function is decreasing.

b) Review Rolle's Theorem and the Mean Value Theorem.

c) Review vertical and horizontal asymptotes and be able to graph functions using calculus concepts without relying on the calculator.

c) The second derivative describes the concavity of a function. If f " is positive, the function is concave up. If f " is negative, the function is concave down. Inflection points are where the concavity of the function changes.

d) There are two "tests" in the chapter for relative extrema.

The first derivative test and the second derivative test. The first derivative test is where you test x values between each critical number to determine if f ' is changing from positive to negative, or negative to positive. The conclusion would be that there is a relative maximum in the first case, and a relative minimum in the second case.

The second derivative test is where you plug the critical numbers into the second derivative. If f " is positive at the c.n. then the function would have a relative minimum there. If the f " is negative at the c.n. then the function would have a relative maximum there.

e) To determine the absolute extrema of a function on an interval, compare the functional values at the endpoints to those of the relative extrema. You can then find the absolute minimum and absolute maximum on the given interval.

f) Make sure that you always go back to the original function when finding y-values for any points on the graph.

REMINDER: calcchat.com has free solutions to odd numbered problems.