From Hardcover Book, Marsden/Tromba, Vector Calculus Let f(x, y) = 5ye^x - e^5x - y^5
A) Show that f has a unique critical point and that this point is a local maximum for f.
B) Show that ff is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g(x) of a single variable, a unique critical point which is a local extremum is necessarily a global extremum. This example shows that this is not the case for functions of several variables).

There are two major tests of readiness for college: the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores in recent years has been roughly normal with mean µ = 20.9 and standard deviation s = 4.8. sat scores are reported on a scale from 400 to 1600. sat scores have been roughly normal with mean µ = 1026 and standard deviation s = 209. reports on a student's act or sat usually give the percentile as well as the actual score. the percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. tanya scores 1260 on the sat. what is her percentile (± 1)?