Math 1337
Sections 3.5 – 4.5
Review for Test #3
1. Page 180 (16 – 25) Find the derivative of each inverse trig function. You must know formulas!
a. y  tan 1 x
b. h(t )  e sin
1
c. y  x cos 1 x  1  x 2
t
2. Page 186 (26 – 35) Find the derivative of each hyperbolic function. You must know formulas!
b. f(x) = sinh(x2)
a. f(x) = x cosh x
c. f(x) = tanh(ex)
3. Page 193 (1 – 33 odd) Use L’Hospital’s Rule (if appropriate) to find each limit.
1  2x
a. lim
x  1  2 x
b. lim
x0
tan x
ln( 1  x )
e. lim  sec x  tan x 
d. lim xe x
x 
x

c. lim
x 0
f. lim csc x 
x
1  cos x
x2  x
g. lim 1  x x
1
x 0
x 0
2
4. a. Page 204 (23 – 35 odd) Find the critical numbers of each function.
ex
i). y 
x
ii). y  6  2 x
iii). f(x) = x∙e2x
b. Page 204 (37 – 47 odd) Find the absolute extrema of f on the given interval.
i). f ( x) 
1
x  cos x on 0,2 
2
ii). f(x) = x3 – 3x + 1 on [−3, 0]
5. Page 210 (11 – 16) Mean Value Theorem
 
a. f(x) = x + 2 cos x on 0, 
 2
b. f(x) = 2x3 – 3x2 – 12x + 24 on [0, 4]
6-8: Page 217 (1 – 10); (23 – 33 odd)
a. Use f(x) = 2x3 – 3x2 – 12x – 5 to find the intervals where the function is increasing and decreasing.
Then use the first derivative test to determine all local maximums and local minimums.
b. Use f(x) = x3 – 18x2 + 10x – 11 to find the intervals where the function is concave up and concave
down. Then find the coordinates of any inflection points.
c. Use the Second Derivative Test to determine all local maxima and local minima for
f(x) = 2x3 – 3x2 – 12 x + 2
9. Page 225 (1, 13, 37, 39, 41) Sketch the graph of the given function showing all pertinent information.
a. Let f(x) be a polynomial function such that f(2) = 5, f '(2) = 0, and f "(2) = 3. Describe the point
(2, 5).
b. Find all vertical asymptotes for y =
x2
. Does this function have any holes? State the coordinates.
x2  4
Sketch the graph.
10. Page 232 (3, 9, 10, 13)
a. Find the points on the hyperbola y2 – x2 = 4 that are closest to the point (2, 0).
b. A gardener wishes to create two equal sized gardens by enclosing a rectangular area with 300 feet of
fencing and fence it down the middle. What is the largest rectangular area that may be enclosed?
c. A cylindrical cup is to be made from 12 square inches of aluminum. What is the largest possible
volume of such a cup?
d. A cherry grower estimates that if 30 trees are planted per acre, each tree yields on average 50
pounds of cherries. If for each additional tree planted (up to 10), the yield is reduced by 1 pound
per tree, how many additional trees will yield the maximum pounds of cherries?