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Problem 2. (20pt) Suppose you look at the student to your left while taking this exam. You notice that they are sweating
Posted: Wed May 11, 2022 5:31 am
by answerhappygod
- Problem 2 20pt Suppose You Look At The Student To Your Left While Taking This Exam You Notice That They Are Sweating 1 (151.88 KiB) Viewed 21 times
Problem 2. (20pt) Suppose you look at the student to your left while taking this exam. You notice that they are sweating profusely, at a rate of roughly 2 cubic inches per minute. The student has an empty cylindrical container on the floor at the base of the desk and the sweat is dripping into the container. The container has a diameter of roughly 3 inches and is 12 inches tall. You wonder how fast the rate of change of the depth of the sweat is in the container. Since you are doing so well on this exam, you decide to take some time to model the problem. What is the rate of change of the depth of sweat in the container when the depth is 2 inches. (Hint: Recall that the volume of a cylinder is the area of the base times the height).
Problem 4. (25pt) Consider the function 1 f(x) = x2 - 4.c + 3 +3 (a) (5pt) Find the critical points of f (Hint: remember that this includes singular points of the derivative).
(b) (5pt) Find the intervals on which f is increasing and decreasing.
(c) (5pt) Find the intervals on which f is concave up and concave down. (d) (10pt) Find the horizontal and vertical asymptotes. (5 pts for vertical, 5 pts for horizontal.)