ch3

1.Calculatey''andy'''.

y=²(4+3)

y''=

y'''=

2.Find the derivative of the given function.

f(x) =42x

1 + 2x

f'(x) =

3.Findf'(x)

for the function.

f(x) =2x³4x+ 1

x²

f'(x) =

4.The given function represents the position of a particle traveling along a horizontal line.

s(t) = 2t³3t²12t+7

fort0

(a)

5.Find the velocity and acceleration functions.

v(t)

=6t26t12

a(t)

=12t6

(b)

6.Determine the time intervals when the object is slowing down or speeding up. (Enter your answers using interval notation.)

slowing down

speeding up

7.The given function represents the position of a particle traveling along a horizontal line.

s(t) =t

4+t²

fort0

(a)

Find the velocity and acceleration functions.

v(t)

=4t2

(4+t2)2

a(t)

=2t(t212)

(t2+4)3

(b)

Determine the time intervals when the object is slowing down or speeding up. (Enter your answers using interval notation.)

slowing down

speeding up

8.The cost function, in dollars, of a company that manufactures food processors is given byC(x) = 200 +9

x

+x²

9

,

wherexis the number of food processors manufactured.

(a)

Find the marginal cost function,MC(x).

MC(x) =

(b)

Find the marginal cost (in dollars) of manufacturing11

food processors. (Round your answer to the nearest cent.)

$

(c)

Find the actual cost (in dollars) of manufacturing thetwelfthfood processor. (Round your answer to the nearest cent.)

$

A culture of bacteria grows in number according to the functionN(t),

wheretis measured in hours.

N(t) =40001 +4t

t²+ 100

(a)

Find the rate of change of the number of bacteria.

N'(t) =16000 (100t2)

(t2+100)2

(b)

FindN'(0),N'(10),N'(20), andN'(30).

N'(0)

=

N'(10)

=

N'(20)

=

N'(30)

=

(c)

Interpret the results from part (b).

Att= 0

hours, the bacteria population is

---Select---

increasing

decreasing

staying constant

. Att= 10

hours, the bacteria population is

---Select---

increasing

decreasing

staying constant

. Att= 20

hours, the bacteria population is

---Select---

increasing

decreasing

staying constant

. And att= 30

hours, the bacteria population is

---Select---

increasing

decreasing

staying constant

.

(d)

FindN''(0),N''(10),N''(20), andN''(30).

N''(0)

=

N''(10)

=N''(20)

=N''(30)

=

Interpret what the answers imply about the bacteria population growth.

Att= 0

hours, the rate at which the bacteria population is changing is

---Select---

increasing

decreasing

staying constant

. Att= 10

hours, the rate at which the bacteria population is changing is

---Select---

increasing

decreasing

staying constant

. Att= 20

hours, the rate at which the bacteria population is changing is

---Select---

increasing

decreasing

staying constant

. Att= 30

hours, the rate at which the bacteria population is changing is

---Select---

increasing

decreasing

staying constant

9.With an initial deposit of $100, the balance in a bank account aftertyears isf(t) = 100(1.16)^tdollars.

What are the units of the rate of change off(t)?

dollars per year

years

dollars

years per dollar

none of the above

Find the average rate of change over [0, 0.5] and [0, 1]. (Round your answers to two decimal places.)[0, 0.5]=

[0, 1]=

Estimate the instantaneous rate of change att= 0.5 by computing the average rate of change over intervals to the left and right oft= 0.5. (Round your answers to four decimal places.)

Interval[0.5, 0.51][0.5, 0.501][0.5, 0.5001]Average rate of change

Interval[0.49, 0.5][0.499, 0.5][0.4999, 0.5]Average rate of change