Math 2250 HW #13
Due 12:30 PM Thursday, November 7
Reading: Hass §4.7–5.1
Problems: Do the assignment “HW13” on WebWork. In addition, write up solutions to the
following problems and hand in your solutions in class on Thursday.
√
1. A right triangle with hypotenuse 8 is revolved around one its legs to produce a right circular
cone. What choice of lengths of the legs of the triangle produce the cone with the greatest
volume? What is this maximum volume?
8
−→
2. Use the Intermediate Value Theorem to prove that the function f (x) = x5 − x + 1 must have
a root, then use Newton’s Method to approximate this root to three decimal places. (Hint:
It’s probably wise to plot this function using a graphing calculator or Mathematica to help
you pick a good starting point for Newton’s Method.)
1