C1-practicetest3-2324
.pdf
School
Wayzata High School**We aren't endorsed by this school
Course
CALC 146
Subject
Mathematics
Date
Jan 4, 2025
Pages
2
Uploaded by HighnessMusicOpossum45
Practice Exam for Exam 2UMTYMP Calculus I Fall 20231. Rob is shoveling snow off the roof of his house in order to form a snow slide. A side-view isshown below:SnowHousexRob shovels the snow steadily, so that the area of this triangular cross-section is changing at arate of 6 ft2/min. He also makes sure that the base of the triangle is always twice the height.Letxbe the distance from the base of the house to the end of the snow slide. At the momentwhen the snow slide reaches the roof (which is when it is 12 ft high), what is the rate of changeofx? Be sure to use the correct units.2. A rectangular page is to contain 24 square inches of print. The margins at the top and bottomof the page are to be 1.5 inches, and the margins on the left and right are to be 1 inch.(a) Draw a picture representing this situation, and label it appropriately.(b) What should the dimensions of the page be so that the least amount of paper is used?3. Letf(x) = 3x5+ 5x4.(a) Find all critical numbers and local extrema off(x).(b) Find the absolute extrema off(x) on the interval [-2,12].4. Evaluate limx→0+x2x.5. For each question below, circle True or False. If it is true, use calculus to explain why it istrue, citing any theorems you use. If it is false, clearly explain why it is false, giving aspecificcounterexample when appropriate.(a) If 0< c <1 andcis the location of the only local maximum offon (0,1), thencis thelocation of the absolute maximum offon [0,1].(b) Supposefis an even function which is differentiable for all real numbers. Then in anyinterval (-a, a) wherea >0, there is somecso thatf0(c) = 0.
Bonus!Sketch the graph of a continuous functiony=f(x) such thatf(1) = 0;f0(x)<0,whenx <-1 orx >3;f0(x)>0,when-1< x <3;f00(x)<0,whenx <-1 or-1< x <5;f00(x)>0,whenx >5.