anything you can help me with i am currently just starting the first problem

Take Home Test B (2.6 and Chapter 3)
You don?t need to print, scan, or submit page 5 (it just has images for reference for two problems)
1. Find dy/dx (or y?) for the following:

4 x 2 ? 2 y 2 + 3 x 2 y = 2 x . Show work.

2. Find the slope of the tangent line to the graph of
work.

3. Determine where the function

f ( x) =

3 x 3 + 5 y 2 + x = 1 at the point (-1,1). Show

1 3
x ? x 2 ? 3 x + 4 is increasing/decreasing using
3

calculus. Show all work including a sign chart and clearly mark your answers.

Increasing on:
Decreasing on:

4. Find the relative extrema of the following function using calculus. Show all work including a
sign chart.

f ( x) = ( x 2 ? 9) 4

Relative maximum occurs at the point: _________

Relative minimum occurs at the point: __________

5. Consider the function

f ( x) = x 2 ? 8 x + 3 .

a. Find the absolute maximum and minimum of the function over the interval [3,6]. Show
all work.

b. Find the absolute maximum and minimum of the function over the interval [0,3]. Show
all work.

6. State whether true or false: If f ' (c) = 0 and f ' ' (c ) is negative, then f (c ) is a relative
minimum.

7. Find the inflection points and the intervals of concavity for the function

f ( x) = 2 x 3 + 5 x ? 1

Show your work.

Concave up on:_______________________________

Concave down on:_________________________________

Inflection point(s): ___________________________
8. Suppose that f ' (c) = 0 and f ' ( x) changes sign from negative to positive at x=c. Which of the
following statements is correct? Circle your answer.
a)

f (x) has a relative min at x=c

b)

f (x) has an absolute max at x=c

c)

f (x) has a relative max at x=c

d)

f (x) has an inflection point at x=c

9. Find the point of diminishing returns for the sales function

S ( x) = 112 + 1.8 x 2 ? 0.1x 3 , where x

represents thousands of dollars spent on advertising, and S is sales in thousands of dollars.
Show your work.

10. Suppose that there is a function f(x) such that its second derivative is

f ' ' ( x) = 6 x( x ? 5) 2 .

Answer the following questions. Show your work below.
A) What are the inflection point(s) of f(x)?

B) For which x-values of f(x) concave up? Concave down?

11. Consider the function shown on the reference page.
a) On which x-intervals is the function concave up?

b) On which x-intervals is the function concave down?

12. Use the image on the reference page. Match the graphs. (No explanations required)
The derivative of a is ______
The derivative of b is ______
The derivative of c is ______
The derivative of d is ______

13. The cost of producing x compact refrigerators is

C ( x) = 2880 + 35 x + 0.2 x 2 dollars. Find the

number of refrigerators that minimizes the average cost if
Applications video for a similar example)

0 ? x ? 150 . (see Chapter 3

Reference Page (don?t need to print, scan or submit)

For question 11:

For question 12: