Question 1

For the function 
f(x)=3(x^4)−4(x^3)
, determine its inflection points. Use fractions. The answers should be in ascending order of 
x
 values.

Accepted Answer

(0;0),  and (2/3;  -16/27)

Answer

(0,0) and (16/27)

Answer

(0; 0) and (-27/16)

Answer

(0,0) and (27/16)

Question 2

For the function 
f(x)=2(x^2)+7x+(−4)
, determine its critical number(s) if exists. Use "DNE" if the function has no critical number.

Accepted Answer

-1.75

Answer

-0.5

Answer

-4

Answer

0

Question 3

For the function 
f(x)=−2x(e^(6x))
, determine its critical number(s) if exists. Use fractions. Use "DNE" if the function has no critical number.

Accepted Answer

-1/6

Answer

-1/2

Answer

-3/12

Answer

-0.5

Question 4

For the function 
f(x)=36x+ (1/x)
, determine its critical number(s) on the interval 
(0, ∞)
, if exists. Use fractions. Use "DNE" if the function has no critical number.

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 5

For the function 
K(x)=6x(e^(8x))
, do the following:

(a) Determine its critical number(s) if exists. (Use 
fractions
 for constants.)

Accepted Answer

-1/8

Answer

-1/2

Answer

-1/4

Answer

-1/5

Question 6

s(x)=5(x^3)−(x^4). Determine its critical number(s) if exists. List from least value.

Accepted Answer

x = 0 and x =3.75

Answer

x=0 and x = -3.75

Answer

x=0 and x= 1/2

Answer

x= 0 and x= -1/2

Question 7

For the function 
g(x)=2−6[(x+2)^(2/3)]
, do the following:

Accepted Answer

-2

Answer

-3

Answer

-4

Answer

0

Question 8

For the function 
K(x)=x[e^(3x)]
, do the following:

(a) Determine its critical number(s) if exists. (Use 
fractions
 for constants.)

Accepted Answer

-1/3

Answer

-1/6

Answer

-1/5

Answer

-1/2

Question 9

For the function 
f(x)=(x^4)−(18x^2)−1
, do the following:

(a) Determine its critical numbers. The answers should be in ascending order.

Accepted Answer

x= -3; 0; 3

Answer

x= 2, 3, 0

Answer

x= 2, 0, 4

Answer

x=3, 5, 7

Question 10

g(x)=(x^3)−3x+2
:

(i(a)) Determine the relative maximum point(s) of 
g
.

Accepted Answer

(-1; 4)

Answer

(0;4)

Answer

(8;44)

Answer

(-1; 44)

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