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Calc 1 4.1

 

<== Calculus 1
Number Question Answer
See the work
1. Find the one critical number of the function
37/15
The work

Point Cost: 2
2. There are two critical numbers for the function .
The smaller one equals:
and the larger one equals:
Smaller one: 3

Larger one: 8
The work

Point Cost: 2
3. Find all critical values for the function:



List of critical numbers:
Two critical values:
(1) -1.05409255338946
(2) 1.05409255338946
The work

Point Cost: 2
4. Find critical number of the function f(x) = 11 x \ln x

x=
x=
The work

Point Cost: 2
5. The critical numbers of the function

f(t) = 5 t^{2/3}+t^{5/3}

are t_1= and t_2= with t_1<t_2.
t_2== -2
t_2== 0
The work


Point Cost: 2
6. Consider the function f(x) = 5 - 6 x^2, \quad -4 \leq x \leq 1f(x) = 5 - 6 x^2, \quad -4 \leq x \leq 1.

The absolute maximum value is

and this occurs at x equals


The absolute minimum value is

and this occurs at x equals
absolute maximum value: 5

occurs at x= 0

absolute minimum value: -91

occurs at x: -4
The work

Point Cost: 2
7. Consider the function f(x) = 2 x^3 + 15 x^2 - 144 x + 2, \quad
- 8 \leq x \leq 4
f(x) = 2 x^3 + 15 x^2 - 144 x + 2, \quad
- 8 \leq x \leq 4.
This function has an absolute minimum value equal to
and an absolute maximum value equal to
absolute minimum value: -241

absolute maximum value: 1090
The work

Point Cost: 3
8. Consider the function f(x) = 6 x^2 - 6 x + 9, \quad 0 \leq x \leq
6f(x) = 6 x^2 - 6 x + 9, \quad 0 \leq x \leq
6.
The absolute maximum of f(x) (on the given interval) is and the absolute minimum of f(x) (on the given interval) is
f(x) absolute maximum: 189
f(x) absolute minimum: 7.5
The work

Point Cost: 2
9. Consider the function f(x) = x^4 - 98 x^2  + 11, \quad
 -6 \leq x \leq 15.
This function has an absolute minimum value equal to
and an absolute maximum value equal to
absolute minimum: -2390

absolute maximum: 28586
The work

Point Cost: 3
10. Find the absolute maximum and absolute minimum values of the function

f(x) = (x-1)(x-7)^3  +    9
on each of the indicated intervals.
Enter 'NONE' for any absolute extrema that does not exist.

(A) Interval = [1, 4].
Absolute maximum =

Absolute minimum =

(B) Interval = [1,8].
Absolute maximum =

Absolute minimum =

(C) Interval = [4,9].
Absolute maximum =

Absolute minimum =
(A)
Absolute maximum = 9

Absolute minimum = -127.69

(B)
Absolute maximum = 16

Absolute minimum = -127.69

(C)
Absolute maximum = 73

Absolute minimum = -72
The work

Point Cost: 3
11. Consider the function f(x) = \displaystyle -rac{x}{3 x^2+1}, \quad 0\le x\le 2.

This function has an absolute minimum value equal to:
which is attained at x=
and an absolute maximum value equal to:
which is attained at x=

absolute minimum value:

x value:

absolute maximum value: 0

x value: 0
The work

Point Cost: 2
12. Consider the function f(x) = xe^{-3 x}, \quad 0\le x\le 2.

This function has an absolute minimum value equal to:
which is attained at x=
and an absolute maximum value equal to:
which is attained at x=
absolute minimum: 0

x= 0
absolute maximum:
x= 1/3
The work

Point Cost: 2
13. Find the absolute maximum and absolute minimum values of the function

f(x) = x^3 - 12 x^2 - 27 x+ 2
on each of the indicated intervals.

(A) Interval = [-2, 0].
Absolute maximum =

Absolute minimum =

(B) Interval = [1, 10].
Absolute maximum =

Absolute minimum =

(C) Interval = [-2, 10].
Absolute maximum =

Absolute minimum =
(A)
Absolute maximum: 16

Absolute minimum: 0

(B)
Absolute maximum: -36

Absolute minimum: -484

(C)
Absolute maximum: 16

Absolute minimum: -484
The work

Point Cost: 3
14. Find the absolute maximum and absolute minimum values of the function

f(x) = rac{x^3}{3} - 7 x^2 + 40 x
on the interval [-2,15].

Absolute maximum =

Absolute minimum =
Absolute maximum = 150

Absolute minimum = -332/3
The work

Point Cost: 3
15. Find the absolute maximum and absolute minimum values of the function

f(x) = 3 x -11 \ln(5 x)
on the interval [1,6].

Absolute maximum =

Absolute minimum =
Absolute maximum = -14.703
Absolute minimum = -21
The work

Point Cost: 2
16. Find the x-coordinate of the absolute maximum and absolute minimum for the function

f(x) = {6} x + rac{18}{x}, \qquad x > 0.
x-coordinate of absolute maximum =

x-coordinate of absolute minimum =
x-coord of maximum: none

x-coord of minimum:
The work

Point Cost: 2
17. Find the x-coordinate of the absolute minimum for the function

f(x) = 2 x \ln(x) - 11 x, \qquad x > 0.


x-coordinate of absolute minimum =
x-coord of minimum: 90.02
The work

Point Cost: 2
18. Find the x-coordinate of the absolute minimum for the function

f(x) = rac{e^x}{x^{4}}, \qquad x > 0.


x-coordinate of absolute minimum =
x-coord of minimum: 4
The work

Point Cost: 2