The graph of Un(x) and Un'(x) w.r.t. x would like:
Assuming zero costs, profit through a consumption bundle cn is given by u(cn). Thus,
Slope of the indifference curve is given by:
Slope of the indifference curve
Slope of the indifference curve is orthogonal to the ratio of the profits through the two points.
Exercise 2 Suppose un()2, the positive square-root function. For this function, the derivative function, ()is the...
Exercise 2 Suppose un(x) = x(1/2), the positive square-root function. For this function, the derivative function, u(x), is the function (1/2)1). In the same graph, sketch x(1/2) and (1/2)i) For this case, express the slope of the indifference through the point (Cu1, Gna) in terms of tuo ratios (T1/T2) and (c2/n1). Interpret the way the slope of the indifference through the point (cn1, Cn2) depends on those two ratios.
Explain in your own words (1). The definition of the derivative of a function f(x) at a point (x1, y1) on its graph. [ It is indicate by f(x)]. (2). Does it exist all the time. (3). How is it related to the slope of the tangent line (4). Give a practical example where the definition is used Note: Two page written project, neatly typed, spellchecked, stapled, and handed in. Deadline: April 26/2019 by 11:59 AM
Explain in your own...
4. (a) A function f has first derivative f'(x) and second derivative 2 f" (x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. 3 marks] (ii) Use the f(x), and the First Derivative Test to classify each critical point.[3 marks] (iii) Use the second derivative to examine the...
please explain how
to do step 5 in matlab commands.
med at x=c. 2 The first derivative Ne Scr We investigate the function f(x) 4 12x3+9x2. >> x-linspace (-3,3) >> y-41x.^4-12*x.^3 >> plot (x,y), grid 9*x."2; + A plot over the interval I-3,3] reveals an apparent "flat section"' with no visible relati extrema. To produce a plot that reveals the true structure of the graph, we replot over the interval [-1,2]: >> x=linspace (-1,2); >> y= 4 * x. ^4-12*x.^3...
2. The function f(SID) takes as an input the student ID number of a student in this room, and returns his or her full name. Is f(SID) invertible? (That is, does it have an inverse function?) If so, what would this inverse function do? If not, why not? 3. The function (SID) takes a UC Merced student's ID number, and returns his or her height, to the nearest inch. Is h(SID) invertible? If so, what would this inverse function do?...
Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function y = f(x) given in the figure. (a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive? (Select all that apply.) OOOO (b) Over what interval(s) (a) through (d) is...
* Note: The most relevant sections of the textbook are 3.1 and 3.2 but the material builds on earlier content 1) Suppose that Nadeem has the same utility function as Lisa did in assignment 1 of U(x,y) - x""ybut the two goods are chickpea curry units/wk (represented by x) and rice units/wk (represented by y). As before, his marginal utility functions for x and y are respectively: MU_(x,y)==0)** [2] and MU,(x, y) =*)*** [2] In assignment 1, the marginal rate...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the...
Problem 4.1 - Odd Bound States for the Finite Square Well Consider the finite square well potential of depth Vo, V(x) = -{ S-V., –a sx sa 10, else In lecture we explored the even bound state solutions for this potential. In this problem you will explore the odd bound state solutions. Consider an energy E < 0 and define the (real, positive) quantities k and k as 2m E K= 2m(E + V) h2 h2 In lecture we wrote...
2. Gini Index Income Decile Income Share 0.05 0.1 0.15 0.2 0.25 0.35 un 0.45 1 a. Graph the Lorenz Curve for the table above. (If it helps to be more precise than the table: the Lorenz curve has a slope of 0.05 from 0 to 0.5 of the income distribution, a slope of 0.1 from 0.5 to 0.8 on the income distribution, and a slope of 0.2 from 0.8 to 1 on the income distribution) b. Calculate the Gini...