Chapter 2, Problem 2.11P

.  what is a Function? Discuss the following concepts of functions with the help of an economic example : 1) Decreasing Function          2) Implicit Function          3) Multi-valued Function 4) Exponential function          5) Logarithmic Function

What are the Least Squares Assumptions? also explain the usage of these Assumptions?

My Moodle My Fa The function f(x, y) = (x + y) – a² – y? – 6xy has stationary points at some of the following points, (x, y). In each case identify whether the point is stationary, and if so find out if it is a maximum, minimum or saddle point. 1. The point (0,0) is 2. The point (1/2, 1/2) is 3. The point (1/2, -1/2) is 4. The point (-1/2,1/2) is 5. The point (-1/2,–1/2) is Next pa - from video in SVG Mock paper Jump to... format

Consider the relationship y = f(x). In this relationship: %3D Oa. y is called the independent variable and x is called the dependent variable. O b. y is called the range and x is called the domain. O c. yis called the dependent variable and x is called the independent variable. O d. y is called the domain and x is called the range.

DERIVATIVE    In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols.                                                                                                 Y = X3 -2X2 +1 X -.333 0 .333 .667 1 1.333 1.667 Y               dy/dx               d2y/dx2                 A function is given above.  The table gives several pre-selected values of the independent variable (X).  Use all of these to have enough to answer questions for this assignment.  Calculate the Y value corresponding to each X value in the table.  Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate worksheet, show how you calculated its Y value.  Use these X,Y pairs also if you chose to do the bonus option. Find the critical values among the given X values…

Refresh your Math & Graphing Skills SOP-A D For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. X-axis Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled The average grade received" and Y-axis should be labeled "The number of hours spent studying". Scenario As the number of hours spent studying rises, the average grade received rises. As the number of hours spent studying falis, the likelihood of getting an A falls. As the number of hours spent watching TV rises, the average grade received falls. True True or False: Line B has a slope of infinity. O False www Relationship Line Y

4. Find the maximum values of the following functions and show whether they are maximized at their maximum values. (a) y= f(x)=10x – x² (b) z=10x+10y-xy-x² - y²

Solve and Select the right answer: In x 1- (10 points] Find the derivative dy/dx if y= 1 (A) 2x2 1. 2n x (C) + 1 (D) 2In x (B) X' 2- (10 points] Find the derivative dy/dx if y=35* +(5x )' (A) y=35* +375 x² (B) y=3*. 5 ln 3+375x? (C) y=3°*, In 3+375x? (D) y=3*. 5ln 3+ x?

Compute the first and second derivatives of the following functions of x. In each case, determine whether the function has any local extremes (maxima or minima) on the domain of nonnegative real numbers – i.e. for x E [0, 0). a. f(x) = 4 + 3x? b. f(x) = x (4x – 3) (9 - 5x) с. f(x) — x2 d. f(x) = In(x) -