# Differential Calculus

Find the interval where the function is increasing and the interval where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in those blanks.)

( , ) (increasing)

( , ) (decreasing)

2. [TanApCalc7 4.1.014.] --/8 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

3 -- 2 0/2

4 -- 2 0/2

-- -- 8 --

Find the interval where the function is increasing and the interval where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in those blanks.)

( , ) (increasing)

( , ) (decreasing)

3. [TanApCalc7 4.1.024.] --/18 points No Response | Show Details Notes

part score total submissions

1 -- 3 0/2

2 -- 3 0/2

3 -- 3 0/2

4 -- 3 0/2

5 -- 3 0/2

6 -- 3 0/2

-- -- 18 --

Find the interval where the function is increasing and the intervals where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in those blanks.)

( , ) (increasing)

( , ) ( , ) (decreasing)

4. [TanApCalc7 4.1.048.] --/8 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

3 -- 2 0/2

4 -- 2 0/2

-- -- 8 --

Find the x-values of the relative maxima and relative minima of the function below. (Enter NONE in any unused boxes. If there are multiple values, enter them in increasing order.)

x = , (relative maxima)

x = , (relative minima)

5. [TanApCalc7 4.2.040.] --/18 points No Response | Show Details Notes

part score total submissions

1 -- 3 0/2

2 -- 3 0/2

3 -- 3 0/2

4 -- 3 0/2

5 -- 3 0/2

6 -- 3 0/2

-- -- 18 --

Determine where the function is concave upward and where it is concave downward. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is concave up or down, enter NONE in those blanks.)

( , ) (concave up)

( , ) ( , ) (concave down)

6. [TanApCalc7 4.2.044.] --/8 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

3 -- 2 0/2

4 -- 2 0/2

-- -- 8 --

Find the inflection point(s), if any, of the following function. (Enter points in order of increasing x-value, typing NONE in any unused boxes.)

( , )

( , )

7. [TanApCalc7 4.2.050.] --/12 points No Response | Show Details Notes

part score total submissions

1 -- 3 0/2

2 -- 3 0/2

3 -- 3 0/2

4 -- 3 0/2

-- -- 12 --

Find the inflection point(s), if any, of the following function. (Enter points in order of increasing x-value, typing NONE in any unused boxes.)

( , ) (smaller x-value)

( , ) (larger x-value)

8. [TanApCalc7 4.3.028.] --/8 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

3 -- 2 0/2

4 -- 2 0/2

-- -- 8 --

Find the horizontal and vertical asymptotes of the graph of the following function. Fill in the blanks. (Enter the values in numerically increasing order. Enter NONE in any unneeded boxes.)

horizontal asymptote: y =

(smaller value)

y =

(larger value)

vertical asymptote: x =

(smaller value)

x =

(larger value)

9. [TanApCalc7 4.3.062.] --/4 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

-- -- 4 --

The average cost per disc (in dollars) incurred by Herald Media Corporation in pressing x DVDs is given by the following average cost function.

(a) Find the horizontal asymptote of C(x).

y =

(b) What is the limiting value of the average cost?

$ per disc

10. [TanApCalc7 4.2.054.] --/8 points No Response | Show Details Notes

part score total submissions

1 -- 2 0/2

2 -- 2 0/2

3 -- 2 0/2

4 -- 2 0/2

-- -- 8 --

Find the relative extrema, if any, of the following function. Use the second derivative test, if applicable. (Enter NONE in any unused answer blanks.)

The relative maximum is at x =

The relative minimum is at x =

#### Solution Preview

The solution file is attached.

Find the interval where the function is increasing and the interval where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in those blanks.)

( , ) (increasing)

( , ) (decreasing)

f(x) = 2 - 10x

f'(x) = -10, which is constant and lesser than 0

f(x) is always decreasing. ANSWERS:

(a) (NONE, NONE)

(b) (-∞, ∞)

Find the interval where the function is increasing and the interval where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in those blanks.)

( , ) (increasing)

( , ) (decreasing)

f(x) = 2x^2 + 9x + 9

f'(x) = 4x + 9

f'(x) > 0 when 4x + 9 > 0, that is, x > -9/4

f'(x) < 0 when 4x + 9 < 0, that is, x < -9/4 ANSWERS:

(a) (-9/4, ∞)

(b) (-∞, -9/4)

Find the interval where the function is increasing and the intervals where it is decreasing. (If you need to enter - or , type -INFINITY or INFINITY. If there is no interval where the function is increasing/decreasing, enter NONE in ...

#### Solution Summary

All questions in the file neatly solved showing all the details. The intervals where the function is increasing and decreasing is determined.