Suppose that V is an open set in Rn that a V, and that f: V

Question:

Suppose that V is an open set in Rn that a ∈ V, and that f: V → R is C2 on V. If f(a) is a local minimum of f', prove that D(2)f(a; h) > 0 for all h ∈ Rn.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:23 AM

See More Questions

Suppose that V is a bounded, nonempty, open set in Rn and that : V Rn is 1 - 1 and continuously differentiable on V with 0 on V. Let W = {Wj}jN be an open covering of V and {j}jN be a Cp partition...
Suppose that T : Rn Rn is a linear transformation and suppose that v is a vector such that T(v) 0 but T2 = T o T). Prove that v and T(v) are linearly independent.
Suppose that V is open in Rn, that a V, and that F : V R is C1 on V. If F(a) = 0 Fxj(a) and u(j): = (x1 . . . . .. . . .-xj-1, xj+1,. . . . . . . . ., xn) for j = 1,2, ...,n, prove that there exist...
1. You are required to compare the results of your printed reports and the results of reports of the MYOB assignment book in your MYOB assignment. If it is assumed that two results of the reports are...
What conditions would help make a percent-of-sales forecast almost as accurate as pro forma financial statements and cash budgets?
Cokes New CEO Battles a Changing Market and its related Challenge Case Summary were written to help you understand the management concepts contained in this chapter. Answer the following discussion...
Have you ever experienced cognitive dissonance? What were the conflicting ideas, attitudes or beliefs you were trying to reconcile? What did you do about it?(pp. 102103)
What is the problem with time lags in technical analysis and why may the analysis lead to self-fulfilling predictions?
Burt's Bee's is deciding whether to invest in a short-term project. If the initial cost to invest today is $12,000 and they are expecting a cash inflow of $14,256 in exactly one year, what would be...
The flywheel of a small punching machine rotates at 360 rpm. Each punching operation requires 2034 J of work and it is desired that the speed of the flywheel after each punching be not less that 95...
Suppose that V is open in R2, that (a, b) V, and that f: V R has second-order total differential on V with fx(a, b) = fy(a, b) = 0. If the second-order partial derivatives of f are continuous at...
Let a, b, c, D, E be real numbers with c 0. a) If DE > 0, find all extrema of ax + by + cz subject to the constraint z = Dx2 + Ey2. Prove that a maximum occurs when cD < 0 and a minimum when cD > 0....
Draw structures corresponding to the following IUPAC names: (a) cis-1, 2-Cyclohexanedicarboxylic acid (b) Heptanedioic acid (c) 2-Hexen-4-ynoic acid (d) 4-Ethyl-2-propylocatanoic acid (e)...
The adjusted trial balance columns of a worksheet for Levitt Corporation are shown below. The worksheet is prepared for the year ended December 31, Complete the worksheet by (a) entering the adjusted...
Derive the commutator $\left[Q_{i}, Q_{j} ight]=i \epsilon_{i j k} Q_{k}$ for the charge defined in Eq. (33.4). Use the charge (33.4) to write the commutator, displaying explicit matrix indices...
Verify that the potential $V(\pi, \sigma)$ can be written as Eq. (33.11), and that if $\epsilon=0$ and the symmetry is implemented in the Wigner mode the masses for the $\pi$ and $\sigma$ fields are...
Figure 5.7 shows a number of yield curves at various points in time. Go to www.treasury.gov, and in the Resource Center at the top of the page click on Data and Charts Center. Find the Treasury yield...
The number of vacation days used by a sample of 20 employees in a recent year In Exercises 2326, use technology to draw a box-and-whisker plot that represents the data set. 3 9 2 17 5 3 2 2 6 4 0 10...
Negligent credentialing and negligent retention have been outlawed under the Restatement (Second) of Torts. True/False
Multiple Choice Questions: 1. The largest component of aggregate demand is? a. Government purchases. b. Net exports. c. Consumption. d. Investment. 2. A reduction in personal income taxes, other...
Find f + g, f g, fg, and f/g and state their domains. 31. f(x) = x + 2x, g(x) = 3x? -1 32. f(x) = VT+x, g(x) = VT-x %3D %3D
Use the graphs of f and g and the method of graphical addition to sketch the graph of f + g. 34. f(x) = x'. g(x) = -x? 33. f(x) x. g(x) = 1/x
Find the functions f o g, g o f, f o f, and g o g and their domains. 35. f(x) = 2x - x. g(x) = 3x + 2 %3D %3D 36. f(x) = 1- x', g(x) = 1/x 37. f(x) = sin x. g(x) = 1- V %3D 38. f(x) = 1 - 3x. g(x) =...
Which of the following accounts will not be closed during the closing process? a. Accounts Recelvable b. Wages Expense c. Fees Earned d. Rent Expense
Clarkson Lumber Company After a rapid growth in its business during recent years, the Clarkson Lumber Company, in the spring of 1996, anticipated a further substantial increase in sales. Despite good...
How do external factors such as changing consumer preferences affect the retail industry?"

Suppose that V is an open set in Rn that a V, and that f: V

Question:

Step by Step Answer:

Suppose D 2 fah 0 0 for some h 0 R 2 Since f is C 2 on V and Choose ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions