(a) From the list of all possible rational zeros of the polynomial, use a graphing calculator or software to graph P(x) to nd the rational zeros. (b) Factor as a product of linear and/or irreducible quadratic factors.
Tuesday, October 24, 2017 Math 2211 Notes Chapter 4.3 - How derivatives affect the shape of the graph • Theorem: - If f’(x)>0, then f is increasing - If f’(x)<0, then f is decreasing - A continuous function can only change sign at f(x)=0 • Consequently, this means that if any function changes sign, it is at f(x) = 0 unless the function is not continuous - Example: • f(x) = x ex Find the increasing and decreasing intervals • = -x e +2xe -x • = e (x)(2-x) • x=0,2 • Therefore, • (-∞,0), (0,2), (2,∞) - Though we don’t quite know which intervals are increasing and which are decreasing. To figure this out, just plug in an easy value from an interval into
