Calc 1 Homework ( pls only math experts)
twex9999
diffpractice.docMath 122B Name ________________________
Section _______
3.1-3.6: DIFFERENTIATION PRACTICE
Find the indicated derivative in each case. You should try to simplify your answers if you can. Try quotient rule on problems 1, 10, 17, and 18.
1.
()
ft
¢
for3
()
1
t
ft
t
=
+
2.
()
fx
¢
for2
3
1
()
x
fx
x
+
=
3.
dz
dx
for34
(1)(5)
zxx
=+-
4.
()
fm
¢
for1
()
sec(2)
fm
m
=
5.
()
fx
¢¢
for5
()32
x
fxx
=×
6.
()
f
¢
G
for6
()
1
f
b
b
G+G
G=
-
7.
dy
dt
for3
ln(ln(2))
yt
=
8.
()
gx
¢
for()
x
gxxe
=×
9.
()
xr
¢
for3
()333
xrrr
r
=+-+
10.
()
hy
¢
forln
()
1ln
y
hy
y
=
-
11.
dz
dm
for2
log(10)
m
z
=
12.
()
fx
¢
for2
()sinh(1)
fxx
=+
13.
()
ft
¢
for1
2
()sin
ft
t
-
æö
=
ç÷
èø
14.
()
g
q
¢
for2
()3tan(4)
g
qqq
=+
15.
()
fx
¢
for(
)
3
()cos1
fxxx
=+
16.
dy
du
for(cot1cot)
yu
p
=+
17.
()
gz
¢
for22
()
az
e
gz
az
=
+
18.
()
fx
¢
for(
)
2
3
()
2
ax
fx
x
=
-
19.
()
at
¢
for4
1cos
()ln
1cos
t
at
t
-
æö
=
ç÷
+
èø
Use the values in the table below to answer the following questions. Support your answers using calculus.
|
|
x |
() fx |
() gx |
() hx |
() fx ¢ |
() gx ¢ |
() hx ¢ |
() fx ¢¢ |
|
|
0 |
0 |
1 |
2 |
-1 |
4 |
-5 |
0 |
|
|
1 |
3 |
2 |
1 |
3 |
-2 |
-4 |
-4 |
|
|
2 |
1 |
0 |
3 |
-2 |
3 |
2 |
1 |
|
|
3 |
2 |
3 |
0 |
4 |
2 |
-3 |
2 |
1. Determine if
()()
yfxgx
=
has a horizontal tangent at1
x
=
.2. Determine if
(())
yhgx
=
is increasing or decreasing at3
x
=
.3. Find the equation of the tangent line to
(())
yfgx
=
at2
x
=
.4. Find
(1)
u
¢
if()()3
uxhx
=+
.5. Determine if
2
(())
yfx
=
is concave up or down at1
x
=
.6. Find the slope of
3
()
gx
y
x
=
at2
x
=
.7. Find
(4)
u
¢
for()()
uxhx
=
.8. Find the slope of the tangent line to
()
gx
ye
=
at0
x
=
.Application Problems:
1. The quantity, q, of ice cream cones sold depends on the selling price, p, in dollars, so we can write q = f (p). You are given that f (5) = 1,000 and f ′(5) = –50.
(a)
What do f (5) = 1,000 and f ′(5) = –50 tell you about the sales of ice cream cones?
(b)
The total revenue, R, earned by the sale of ice cream cones is given by R = pq. Find .
(c)
What is the sign of ? If the ice cream cones are currently selling for $5, what happens to revenue if the price is increased to $6?
2. A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20 miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by
where k1 and k2 are positive constants which depend on the quantity of smoke each stack is emitting. For what value of is
?
