Practice question: Find f(3) if 12 fx) = x2 . 2: Solution: To evaluate f(3), we simply plug in the value of 3 for x in the expression: f17) = 32 .2 = 7. Find f'(3) f'(3) represents the taking the first derivative of the expression and evaluating at x = 3: f'(x) = (2)3 (2-1) = (2)3 f'(3) = (2)3 = 6 Question: Find f(7) if f(x) = x2 + 7: f(7) = find f'(7) f'(7) =
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- Hello. May I ask how did you get the values? Were those only assumed values? Can you also explain how did you make the normal form thoroughly?Please find the effect of Y and r if there is a decrease in the tax rate. Use the following equations and evaluate the total derivative.Is this right or wrong (The question is the screenshot) (A) We want to minimize the cost function C(x, y) = 9x + 12y subject to the constraint U(x, y) =x (y + 3) = 128.9 and non-negativity constraints × ≥ 0 and y ≥ 0 We set up the Lagrangian: L(x, y, λ) = C(x, y) - λ(U(x, y) - 128.9) Now, we calculate the partial derivatives with respect to x, y, and 1: ∂L/∂x = 9 - λ(y + 3) ∂L/∂y = 12 - λX ∂L/λ = 128.9 - U(x, y) Setting these partial derivatives equal to zero, we have: 9 - λ(y + 3) = 0 2 12 - λx = 0 128.9 - x(y + 3) = 0 From equation 2, we get λ= 12/x. Substituting A into equations 1 and 3: 9 - (12/x)(y + 3) = 0 2. 128.9 - xY - 3x = 0 Now, we can solve this system of equations simultaneously. Let's start by solving equation 2 for X: 128.9 - xy - 3x = 0 xy = 128.9 - 3x Now, substitute this into equation 1: 9 - (12/x)(y + 3) = 0 9-(12/x)(128.9 - 3x + 3) = 0 9- (12/x)(131.9 -3x) = 0 9 -1,582.8/x + 36x = 0 Multiply through by x to get rid of the fraction: 9x - 1.582.8 ÷…
- The variable shown on the vertical axis is _________ . The units for the variable on the horizontal axis are __________ . There are two ways to view the information presented on the graph. First, the graph tells us the amount a person with a certain income is likely to spend on a car, and second, it tells us the probable income of a person who spent a certain amount on a car. For example, if an individual earned $40,000 last year and purchased a new car, you would expect that person to have paid about _________ for the car. Similarly, if someone just paid $25,000 for a car, you could use this graph to estimate that this person's income was probably around __________ .Obtain the second derivative of the function: y = 2 – 5x4 + 3/2x2. 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
- Colton is trying to figure out when two buses traveling at different speeds will pass one another. The buses are traveling in the same direction and begin 3 miles apart. He has defined variable tt as follows: Let tt represent the time in hours. Is this a good variable definition? YES OR NO ? IF NO than explain why?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…In the formula ke >= (D1/P0) + g, what does (D1/P0) represent?
- Q2B. Which of the following are limitations of using Impulse Response Functions(IRFs) in time series analysis?i. IRFs are only valid for linear time series models.ii. IRFs assume that the underlying time series is stationary.iii. IRFs can provide information about the short-term dynamics of the relationshipbetween variables, but they do not capture longer-term effects or otherimportant aspects of the relationship.iv. IRFs depend on the specification of the model used to estimate the relationshipbetween variables.A curve is defined implicitly by the equation 2y = 1 + xy^3.(a) Check that (1, 1) is a point on the curve.(b) Find the value of y′ at this point, using partial derivatives.(c) Find the equation of the tangent line to the curve at this point.Use the IS Equation, S(y) + M(y) = I(r) + X, to derive the slope of the IS curve. Describe the significance of points to the left and right of this schedule. Please type out the correct answer ASAP with proper explanation within 40 min. Thank you .