Anything you can help me with would be much appreciated but i also need work with the answers.
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
3. Determine where the function
f ( x) =
3 x 3 + 5 y 2 + x = 1 at the point (-1,1). Show
x ? x 2 ? 3 x + 4 is increasing/decreasing using
calculus. Show all work including a sign chart and clearly mark your answers.
4. Find the relative extrema of the following function using calculus. Show all work including a
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
b. Find the absolute maximum and minimum of the function over the interval [0,3]. Show
6. State whether true or false: If f ' (c) = 0 and f ' ' (c ) is negative, then f (c ) is a relative
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.
f (x) has a relative min at x=c
f (x) has an absolute max at x=c
f (x) has a relative max at x=c
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: