Consider the following function.
f(x)= {4x+3, x ≤ −1
{x^{2}2, x > −1
a) Find the critical numbers of f. (Enter your answers as a commaseparated list.)
x = 0, 1
b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing: (?, ?) ***the answer is NOT (0, ∞)
decreasing: (1, 0)
c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum (x, y) = (?, ?)
relative minimum (x, y) = (0, 2)
Consider the following function.
(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing 

decreasing 

(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum  (x, y)  = 



relative minimum  (x, y)  = 
Consider the following functions for consumption and investment: C = 1,000 + (2/3)*(Y – T) and I = 1,200 – 100*r. Furthermore, Y = 8,000, G = 2500, T = 2,000.
Answer all four.
int f(int n) {
if ((a >= b) && (c < b)) return b;
else if (a >= b) return f(a, c, b);
else return f(b, a, c);
}
First, draw the graph defined by that adjacency matrix, and label the vertices of the graph with 1, 2, 3, …, 6 so that vertex i corresponds to row and column i.
Second, Give a coloring of the vertices (color the graph) that uses the minimum number of colors. Prove with explanations that your given coloring is the minimum coloring.
where

a  b 


c  d 

a_{1}  b_{1} 


c_{1}  d_{1} 
and

a_{2}  b_{2} 


c_{2}  d_{2} 
in
and the scalar c. (Give all answers in terms of
=
=
=
=
=
=
f(x)= (x^{2 }– 3x +2)/(x^{2}1)
Consider the following functions.
f(x)= 1/3x^23/4x
g(x)=1/2x+5/6
h(x)=1/4x^25/8x+2/5
Part a. Amarion wants to determine f(x)g(x)h(x) . His steps are shown below, but he made a mistake.
In which step did he make a mistake and what was the mistake?
Amarion made a mistake in
Step 1:(1/3x^23/4x)(1/2x+5/6)(1/4x^25/8x+2/5)
Step 2: (1/3x^25/4x5/6)(1/4x^25/8x+2/5)
Step 3: 1/12x^215/8x13/30
part b. because
a. he did not distribute the 1 to all terms
B. he did not get a common denominator for all the terms
C. he did not change the exponents when combining like terms
Consider the following function main:
Int main()
{
int inStock[10][4];
int alpha [20];
int beta[20];
int gamma[4]= {11,13,15,17};
int delta [10] = {3,5,2,6,10,9,7,11,1,8};
}
a) Write the definition of the function setZero that initializes any onedimentional array of type int to 0.
b) Write the definition of the function inputArray that prompts the user to input 20 numbers and stores the numbers into alpha.
c) Write the definition of the function doubleArray that initializes the elements of beta to two times the corresponding elements of alpha. Make sure that you prevent the function from modifying the elements of alpha.
d) Write the definition of the function copyGamma that sets the elements of the first row of inStock to gamma and the remaining rows of inStock to three times the previous row of inStock. Make sure that you prevent the function from modifying the elements of gamma.
e) Write the definitions of the function copyAlphaBeta that stores alpha into the first five rows of inStock and beta into the last five rows of inStock. Make sure that you prevent the function from modifying the elements of alpha and beta.
f) Write the definition of the function printArray that prints any onedimensional array of type int. print 15 elements per line.
g) Write the definition of the function setInStock that prompts the user to input the elements for the first column of inStock. The function should then set the elements in the remaining columns to two times the corresponding elements in the previous column, minus the corresponding element in delta.
h) Write C++ statements that call each of the functions in parts a through g
i) Write a C++ program that tests the function main and the functions discussed in parts a through g. (Add additional functions, such as printing a twodimensional array, as needed.)
please i need complete answers from question a) till i) in c++ programming language
C) Find the values of x in the domain of h such that h ′(x) does not exist. (If an answer does not exist, enter DNE.)
D) Find the critical numbers of the function. (If an answer does not exist, enter DNE.)
Consider the following function: f (x) = (x − 4)(x + 2) / (x+4)(x+2
1.For what values of x is f(x) continuous? State your answer using interval notation
2.Find the following limits (if they exist)
a. lim f (x) x→ −4
b. lim f(x) x→ −2
3.Does f(x) have any vertical asymptotes? If yes, then write down the equation of the vertical asymptote(s)? Show working or give a reason for your answer.
4.Does f(x) have a horizontal asymptote? If yes, then write down the equation of the horizontal asymptote? Show working or give a reason for your answer.
Consider the following function.
f(x)= {4x+3, x ≤ −1
{x^{2}2, x > −1
a) Find the critical numbers of f. (Enter your answers as a commaseparated list.)
x = ?
b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing: (?, ?)
decreasing: (?, ?)
c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum (x, y) = (?, ?)
relative minimum (x, y) = (?, ?)
Multiple Choice Question
Consider the following function. What is the purpose of the function f? Please do explain and describe in details all possible answers for this function given below.
int f(int n) {
if ((a >= b) && (c < b)) return b;
else if (a >= b) return f(a, c, b);
else return f(b, a, c);
}
a. To find the maximum number between a, b, and c.
b. To find the middle number between a, b, and c.
c. To find the minimum number between a, b, and c.
d. None of the other statements.
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