MATH 140 Midterm: MATH140 JOHNSON-G FALL2008 0203 MID EXAM 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: All

Document Summary

Your solutions should read nicely and be leg- ible. They should not be composed of regurgitated fragments of your mind scattered about the page: let f (x) = [8 pts] (e) find the coordinates of all relative extreme values and in ection points. [8 pts] (f) sketch the graph of f (x). [8 pts: find all functions f (x) such that f (x) = cos(2x) + sec x tan x + 1 and f ( ) = 0. [15 pts: find the maximum area of a rectangle in the rst quadrant with one vertex at the origin and the opposite vertex on the graph of y = e x. [10 pts] (b) let f (x) = x3 + x 1. Use rolle"s theorem to explain why f (x) can not have more than one x-intercept. (hint: suppose there were 2. What would rolle"s theorem say about f (x)?)