Week 10: Week ln Review MATH 131
4..3-5.5 for EXAM lll
DROST
Section 4.3
Section 4.6
1. f(x) =2*3x -
a.
x3
Find the interval(s) over which
/(r)
7.
area 1000 m3, whose perimeter is as
smallas possible.
is decreasing.
b.
Find the interval(s) over which
f(x)
is concave up.
8.
c. State the x-values ofany point{s) of
ffi,
Give the x-coordinate of the inflection
point(s) of /,
a. given the graph
b. given the graph
given the graph
c.
The rate at which photosynthesis takes
place for a species of phytoplankton is
modeled by: P =
where I is the
light intensity (measured in
footcandles). For what light intensity is
inflection.
2.
Find the dimensions of a rectangle with
P maximized?
/(x).
is f'(x).
is f"(x).
is
9.
A rectangular storage container with an
open top is to have a volume of 10 m3.
The length of its base is twice the width.
Material for the base costs S1O/m2, and
material for the sides costs S6/m'z. rind
the cost of materials for the cheapest
such container.
Section 4.8
10. Find the general antiderivative
f (x) = Bxe * 3x1/z * ex -
of
lnx
*
ez
11. Find the antiderivative F if
3.
Given
f' (x) = (x + 2)2(x- 4)3(x - 1)s
On what interval(s) is f (r) increasing?
f(x) - 4 g'
3x(L + x2)-7, where
F(1) =
f " (x) = -2 * LZx 12x2, f(o) = 4, f' (0) = 12.
12. Find
/
when
Section 4.2
Section 5.1
4.
5.
6.
Find the critical number(s)of
f(x)=x3+6x2-15r.
Find the absolute maximum extrema
f (x) =
x'1T77, ?L,21.
Find the absolute extrema
f (x) = x
-lnx,
I%,21.
of
of
13. Find an upper estimate to the area
under the curve using four rectangles
on the interval [0,8].
t
17. A table of values is shown. Use it to
find the upper and lower estimates for
u
lil f f.l
dx using Riemann sums and
five rectangles.
'l
x
2
f(x)
14. Given f (x) = z
the interval [1,5].
-
3lnlxl , find
Ma on
t4
-5
18
-2
22
26
30
1
3
8
18. Use the midpoint rule to approximate
tft"f,xTe-xdx, n=4.
15. The velocity graph of a braking car is
shown. Use it to estimate the distance
traveled by the car whib the brakes are
applied, using 16 and R5.
vrIt
10
-12
st
Section 5.3
Ls.
I:u - L)(zy + 1) dy
za.
t;
zt.
filzx -
Lox dx
1l dx
Section 5.4
22. Let s(x) =
I{
fft> at
10
Section 5.2
o
16. The graph of
IlrS(iax
g(x)
is
6
shown. Estimate
4
with six subintervals using:
2
.2
-4
-5
.8
-10
23. Find the derivative of
/(r)
=
24. Find the derivative of g(r) =
fi'/7
*
a,
Ii *,
dt
Section 5.5
zs.
! e*,/TW
26.
I
g-a^
zt. 'lL
z5+1
dx
az
a7