Reference no: EM13976027
1) Suppose f(π/4) = ½ and f'(π/4) = -3, and let g(x) = f(x)sin(x) and h(x) = cos(x)/f(x). Find the following derivatives:
a. g'(π/4)
b. h'(π/4)
2) If f(3) = 4, g(3) = 2, f'(x) = -6 and g'(x) = 5, find the following numbers.
a. (f+g)'(3)
b. (fg)'(3)
c. (f/g)'(3)
d. (g/f)'(3)
3) Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the following whose graphs are shown.
a. Find P'(2)
b. Find Q'(7)
4) If g is a differentiable function, find an expression for the derivative of each of the following functions
a. y = x3g(x)
b. y = g(x)/x4
c. y = x2/g(x)
d. y = 1+xg(x)/ √x
5) If h(x) = √(3+2f(x)), where f(2) = 3 and f'(2) = 5, find h'(2).
6) A table of values for f, g, f' and g' is given.
| x |
f(x) |
g(x) |
f'(x) |
g'(x) |
| 1 |
3 |
2 |
4 |
6 |
| 2 |
1 |
8 |
5 |
7 |
| 3 |
7 |
2 |
7 |
9 |
a. If F(x) = f(f(x)), find F'(2).
b. If G(x) = g(g(x)), find G'(3).
c. If H(x) = g(f(x)), find H'(2).
7) If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2). Use the graph of f to estimate the value of each derivative.
a. h'(2)
b. g'(2)
8) Suppose f is differentiable on R and α is a real number. Let F(x) = f(xα) and G(x) = [f(x)]α. Find expressions for:
a. F'(x)
b. G'(x)
9) If g is a twice differentiable function and f(x) = g(x3) sin(x), find f" in terms of g, g', and g".
|
What you plan to accomplish cross-culturally for mnc
: You will identify a product or service to be "exported-to or manufactured-in" a foreign country of your choosing and develop an individual written Cross-Sectional Cultural Management Plan and Presentation. The paper should be 12 - 13 pages in leng..
|
|
Explain why you chose these three strategies and not other
: Explain what you can do to develop these skills. Describe a plan for how you would develop these skills.
|
|
When the rent-a-limo company negotiates
: When the Rent-A-Limo Company negotiates its new labor contract it finds that the wages it must pay drivers have increased. How does this wage hike affect the Rent-A-Limo Company's average fixed cost, average variable cost, average total cost, and mar..
|
|
Ethical dilemmas associated with offshoring are plenty.
: .Ethical dilemmas associated with offshoring are plenty. Choose one of these dilemmas and make a case either defending your firm's offshoring activities or arguing against such activities
|
|
Find an expression for the derivative of each functions
: If g is a differentiable function, find an expression for the derivative of each of the following functions
|
|
Differences between the three normative theories
: For this discussion, you will analyze the differences between the three normative theories. Read the following three CNET.com articles regarding the Sony Playstation Network information breach: The Playstation Network Breach Sony Online Entertainm..
|
|
What value of b is required for these ions to hit detector
: A mass spectrometer, sketched below, is a device used to separate different ions. Such ions with a well-defined velocity vo enter through a slit into a region of uniform magnetic field B, where they follow a semicircular path until they strike a d..
|
|
The economics of health and health care
: The local Chamber of Commerce where you live has learned that you are taking this course. They have asked you to come and be a guest lecturer about health system reform; specifically they are very curious about the Patient Protection and Affordabl..
|
|
A price-setting process is a sophisticated multi-step
: A price-setting process is a sophisticated multi-step approach that has to take into account the external environment, competitors, and consumer demand for the product, as well as internal factors such as operating costs.
|