Math 251
This is our fourth test: uplifting, fifty-minute, four-page, 100-point. It covers chapter
four of Calculus—Early Transcendentalsi(6ed) by J. Stewart. All parts of all problems
are four points unless otherwise indicated. Clearly indicate your answers.
1. Find two positive numbers whose product is 50, and the sum of the first plus twice
the second is a minimum. (6 points)
2. Suppose Dr. Caldwell is on the top of a 13 foot ladder cleaning
his gutter. His mischievous son Aaron pulls the bottom of the
latter away from the wall at a rate of 1 foot per second. How
fast is the top of the ladder descending when the bottom of the
ladder is 5 feet from the wall. (8 points)
3. Evaluate the integral ⌡
⎮
⌠
4
−4
16 − x2 dx by interpreting it in terms of an area.
