Math 1100
Chapters 10–11 Review
30 October, 2013
Name:
The questions below are intended as a partial review. You should also refer to
your written homework and quizzes (and, to a lesser extent, your WebAssign
work) as you study for the exam.
1. Consider the function
f (x) = 4x5 − 5x4 − 40x3
(a) Find all critical values of f (x).
(b) Find all intervals where f (x) is increasing.
(c) Find all intervals where f (x) is decreasing.
(d) Is f (x) concave up or down at x = −1?
(e) Find all relative maxima of f (x).
(f) Find all relative minima of f (x).
(g) Find the x-values of all points of inflection of f (x). (Some are irrational.)
(h) Find the absolute maximum of f (x) on the interval [−1, 2]
(i) Using the information above, sketch a graph of f (x). Label your axes to show scale.
2. A cowherd has 1200 feet of fence. He wishes to enclose a rectangular pasture next to a
river, so he need only fence three sides. What dimensions will give him the maximum
area?
3. Find
dy
.
dx
(a)
y = ln
x4
x−1
(b)
y = x2 e6x
3 −x
(c)
3xy = 2y 2 + x
4. The radius of a sphere is increasing at the rate of 2 cm/s. At what rate is the surface
area increasing when the radius is 15cm? (Recall that the surface area of a sphere is
given by A = 4πr2 .)