Math 2250 HW #11
Due 12:30 PM Thursday, October 24
Reading: Hass §4.2–4.4
Problems: Do the assignment “HW11” on WebWork. In addition, write up solutions to the
following problems and hand in your solutions in class on Thursday.
1. An airplane begins its descent toward the runway when it is 4 miles from the touchdown point
and at an altitude of 1 mile.
(a) Find a, b, c, d so that the cubic function f (x) = ax3 + bx2 + cx + d describes a smooth
glide path for the airplane as pictured below (Hint: you have 4 pieces of information
about the function f (x). If you translate these pieces of information into 4 equations,
you will be able to solve for the four unknowns a, b, c, and d.)
(b) Assume the plane follows the path you found in part (a). When is the plane descending
at the greatest rate?
H-4,1L
1
æ
-4
-3
-2
-1
æ
2. Determine whether the following statements are true or false. If the statement is true, explain
why. If it is false, give an example which shows that it is false (called a “counterexample”).
(a) The sum of two increasing functions is increasing.
(b) The product of two increasing functions is increasing.
3. Use your accumulated calculus skills to sketch the graph of the function
g(x) =
x
.
1 + x2
Be sure to label all intercepts, local minima, local maxima, inflection points, asymptotes,
absolute minima, absolute maxima, etc.
1