See the attached file for full description.
40) The value of a certain automobile purchased in 1997 can be approximated by the function v(t)=25(0.85)^t , where t is the time in years, from the date of purchase, and v is the value, in thousands of dollars.
(a) Evaluate and interpret v(4).
(b) Find an expression for v1(t) including units.
(c) Evaluate and interpret v1(4).
(d) Use v(t), v1(t) and any other considerations you think are relevant to write a paragraph in support of or in opposition to the following statement: From a momentary point of view, it is best to keep this vehicle as long as possible".

56) Let f(v) be the gas consumption ( in liters/km ) of a car going at velocity v( in km/hr). In other words , f(v) tells you how many liters of gas the car uses to go one kilometer , if it is going at a velocity v, you are told that
f(80)=0.05 and f1(80)=0.0005.

a) Let g(v) be the distance the same car goes on one liter of gas at velocity v. what is the relationship between f(v) and g(v) ? find g(80) and g1(80).
b) Let h(v) be the gas consumption in liters per hour. In other words, h(v) tells you how many liters of gas the car uses in one hour if it is going at velocity v. what is the relationship between h(v) and f(v)?
Find h(80) and h1(80).
c) How would you explain the practical meaning of the values of these functions and their derivatives to a driver who knows no calculus?

Y= (1 + 1/x)^1/4
Got the 1st derivative to be Y'= 1/4 (1+1/x)^-3/4 * (-1x)^-2
Is that correct?
Now I need the 2nd derivative, I am completely lost on this. Please work out clearly.

Q3) The following ranked data represent the number of English-language Sunday newspapers in each of the 50 states as of February 1, 1996:
2 3 3 4 4 4 4 4 5 6 6 6
7 7 7 8 10 11 11 11 12 12 13 14
14 14 15 15 16 16 16 16 16 16 18 18
19 21 21 23 27 31 35 37 38 39 40 44
62 85
Construct a box plot for the data. Characterize th

Please solve the problems:
1. If p is price in dollars and q is quantity, demand for a product is given by q = 5000e^0.08p
a. What quantity is sold at a price of $10?
b. Find thederivative of demand with respect to price when the price is $10 and interpret your answer in terms of demand.
2. The demand for a product is

Describe how an advanced nurse will interpret and apply theory in a practical environment (i.e., in leadership). Please give one reference in APA format

1.) compute thederivative of f(x)= arctan (x^2)
2.) compute thederivative of f(x)= ln(x^2/(2+x))
3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

Let f(x) be a continuous function of one variable.
a) Give the definition of thederivative.
b) Use this definition to find thederivative of f(x)=x^2+2x-5
c) Evaluate f'(2)

What's the problem with studying meaning? Why is it relevant to adult development? How do people derive a sense of meaning? How does Amundson discuss meaning over the life span? What are your thoughts?