Determine the zeros of f'' (looking for inflection)
Draw a real number line, and indicate the "interesting" parts of the
domain on the line.
Below the line are three lines for f, f', and
f''. On each line mark places where the corresponding function
is either zero or undefined (with double vertical bars).
Indicate the sign of each function between zeros and bars.
Use the four "canonical" function shapes to indicate the shape of the
function for each sign combination of f' and f''.
Describe asymptotic behavior
Let's see how this works on an example or two.
Examples:
#57 and 58, p. 217
#40, p. 217
#79, p. 218
Questions over the Directed reading handout, Section 4.5 (html)(pdf)?
Section 4.6: Optimization (putting it all together)
Folks, this is why calculus is so important. If not for problems
like these, calculus wouldn't be so much fun!;)