The United States wine consumption can be modeled by the function f(x)=0.004x^2-0.094x+2.607 where x represents the year since 1980 and f(x) represents the number of gallons of wine consumed per person: a. Evaluate f(25)  b. In what year can we expect to find the lowest amount of wine consumption per person? How much wine per person was consumed that year?  c. In which years did the US consume 2.5 gallons of wine per person?

Q: The assets A of public pension funds (in billions of dollars) can be approximated by the function…

A: x=3 corresponds to 2003.So, 2013 is 3+(2013-2003)= 3+10=13 year

Q: Differentiate the function. 3 + 6x g(x) 7 - 2x g'(x) =

A:

Q: Find f(-2) for f(x)=3x2^x

A: f(x) = 3x2^x we can also write this as f(x)=3x(2x)

Q: Find (f-1) (a). f(x) = 5x3 + 3x2 + 6x + 7, a = 7 (F-1)(a) =

A:

Q: Differentiate the function. f(x) = x3 - 4x + 6

A:

Q: 4. Given the function y = (3 - 2x²)/(1- x -2x?), (a) Find the difference quotient Ду/Дх.

A: Topic:- Difference quotient

Q: Differentiate the function f(x) − x3 - 4x + 6

A:

Q: Find f(-3) for f(x) = x² – 3x + 3

A: Given f(x)=x2-3x+3 To find f(-3) we put x=-3 in the above function.

Q: Find the difference quotient for f(x) = 4x².

A: To find the difference quotient for:f(x)=4x2 Solution: We know, the difference quotient for a…

Q: Find where function is increasing and decreasing, and graph the function. f(x)= x4-10x3-33x2+90x+216

A: The given function is

Q: Find Relative extreama of function 3. 9K-3xータx+1

A:

Q: Find (f- g)(1) when f (x)= -3x2 + 4 and g (x)= a- 4.

A: Given :

Q: Do f(x) = 2x2 - 1 and h(t) = 2t2 - 1 represent the same function? why or why not

A: The two given functions are

Q: Find x-intercept of: f(x) = -2x2 - 5x + 1

A:

Q: Find f"(x). f(x) = 6x- 14x-

A: Topic = Derivative

Q: Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a month from an…

A:

Q: Find (f-1)'(a). f(x)=5x3+4x2+5x+2, a=2

A:

Q: Graph the function. f(x) =  1/4x2

A: The graph is given below

Q: Differentiate the function  g(x)=7/4x2-3x=12

A:

Q: Find f(10) if f(x) = 3x – 10.

A: Given,            f(x) =3x - 10

Q: Find f. f"(x)  =20x3 -12x2 +6x

A: Consider the provided function, f''x=20x3-12x2+6x Find  fx. Integrate both the sides with respect to…

Q: Find the value of f(x)=-16x3+18x2-x+2 at x= -2

A: Given: fx=-16x3+18x2-x+2 To Find:  The value of fx at x=-2

Q: Differentiate the function. f(x)  =x3 -4x +6

A: To Determine: differentiate the function  Given: we have a function f(x)=x3-4x+6 Explanation:…

Q: Is f(x)=4x-3 a one-to-one function?

A: That's easy. Have a good day!!!

Q: Find the difference quotient of f(x) = −2x2 + x + 1.

A: We have to find the difference quotient of the given function.

Q: The total revenue for Fred's Estates LLC is given as the function R(x) = 100x - 0.4x2. where x is…

A:

Q: Determine the end behavior of the function f (x) : x³ + 3x2- x - 3

A:

Q: 2. How does the function f(x) = -4x + 3x3 behave as x -00 and x 00?

A: The objective is to describe the behaviour of the given function in the ends .

Q: Find (f-1)'(a). f(x) = 4x3 + 3x² + 5x + 2, a = 2 (f-1)'(a) =

A:

Q: Find the points of inflection of the function f(x)=2x4−3x.

A: Inflection point is a point on the graph of function f(x), where the second derivative f''(x) is…

Q: Find f(-2), when f(x) = -0.5x + 12

A: Given that f(x) = -0.5x + 12  To find: f(-2)

Q: Differentiate the function. y= 1/(3x+13)^

A: The given function is  y = 13x+132

Q: Find the domain of the function V5 +4x f(x) = x2 – 36 and write your answer in interval notation.…

A:

Q: Describe the long run behavior of f(x)=-2(4)x+4

A:

Q: if (gof)(- 1) = 3 and g(x) = 4x 1, find f(-1) :

A: Given that (gof)(-1)=3 and g(x)=4x-1 find f(-1)

Q: Find the difference quotient of f(x) = −2x2 + x + 1

A: For the difference of quotient ,  (f(x+h) -f(x))/(h)

Q: Find (f-1)'(a). f(x) = 4x3 + 4x² + 8x + 4, a = 4

A: Derivative of inverse of a function

Q: Find f(-8), if f(x) = x² + 5x - 27

A: The given function is: f(x)=x2+5x-27

Q: Find (f-1)'(a). f(x) = 3x3 + 3x2 + 4x + 2, a = 2 (f-1)'(a) =

A: The given function is; f(x)=3x3+3x2+4x+2  and a = 2 When x = 0, f(0) = 0 +0 +0 + 2 f(0) = 2 The…

Q: rewrite in polynomial function, show your solution. f(x)=(x+3)(x+2)

A:

Q: 4) Is y = -3x² + 12, x 20 a one-to-one function? Why or why not?

A: For one -one function F(x1)=F(x2) then x1=x2

Q: Find the domain of the function. h(x) = 2x/  (x2 - 16)

A: Domain of the function is the set of all values of x for which function is defined.

Q: Find (f-1)'(a). f(x) = 5x3 + 4x2 + 6x + 1, a = 1

A: Topic:- application of derivatives

Q: Two hot air balloons are traveling along the same path away from a town, beginning from different…

A: Given: Henry's balloon begins 15 miles from town and is 31 miles from town after two hours. The…

Q: Use the graph to write the formula for a polynomial function of least degree.

A: Given that by using graph we need to write the formula of a polynomial of least degree. Now,  By…

Q: Describe the end behavior of f (x) = x³ – 4x² + x + 6 -

A:

Q: If f(x) = 10x + 17, find f'(-3).

A: Given,  f(x)=10x+17 f'(x)=10

Q: Write the equation of the polynomial function, f (x), in the graph on the right. Remember to solve…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.