Question: Suppose that F: R R has a second symmetric derivative at some x0. Prove that if F(x0) is a local maximum, then D2F(x0) <

Suppose that F: R → R has a second symmetric derivative at some x0. Prove that if F(x0) is a local maximum, then D2F(x0) < 0, and if F(x0) is a local minimum, then D2F(x0) > 0.

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If Fx 0 is a local minimum then F... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

741-M-N-A-D-I (822).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Helen Derby borrowed $150,000 to acquire a parcel of land to be held for investment purposes. During the current year, she reported AGI of $90,000 and paid interest of $12,000 on the loan. Other...

Suppose that f : R R satisfies f(x + y) = f(x) + f(y) for each x, y R. a) Show that f(nx) = nf(x) for all x R and n Z. b) Prove that f(qx) = qf(x) for all x e R and q Q. c) Prove that f is...

Suppose that f : R (0, ) satisfies f(x + y) = f(x)/(y). Modifying the outline in Exercise 3.3.8, show that if f is continuous at 0, then there is an a (0, ) such that f(x) = ax for all x R. (You...

Suppose that f : R R is differentiable at c and that f(c) = 0. Show that g(x) := |f(x)| is differentiable at c if and only if f(c) = 0.

1. Suppose that F : R ---+ R has a second symmetric derivative at some Xo. Prove that if F(xo) is a local maximum, then D2F(xo) ::; 0, and if F(xo) is a local minimum, then D2F(xo) 2: O.

Hi, can someone please help me with these three problems? thanks! I added the concepts that are provided in my assignment. Hope it can help. thanks! MCS 4. When one looks at statistics measuring the...

D Question 2 1 pts Critical numbers Reminder: In our class, when we consider a function that is defined on a closed domain, the endpoints of the domain are included in the collection of critical...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Math 104A Homework #3 Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made....

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

#detailed explanations plz. 8. A kite is rising vertically at a constant speed of 2 m/s from a location at ground level which is 8 m away from the person handling the string of the kite. kite V 8m...

Zipper has N links: each link has a state in which it is closed with energy 0 and a state in which it is open with energy . We require, however, that the zipper can only unzip from the left end, and...

If y = ex, and y2 = e* are solutions for a certain differential equation then, 1) The Wronskian W is equal to 012x5 O-2 O-4 2) Based on the above answer, the two solutions are considered to be...

14.2 Using Fig. 14.69, design a problem to help other students better understand how to determine transfer functions. V +1) R www R C + Vo

On January 1, 2020, Sheffield Inc. sold computer equipment to Shamrock Co. The sales price of the equipment was $526,000 and its carrying amount is $397,000. Record any journal entries necessary for...

ColAlta Pipeline, Ltd. is a Canadian corporation based in Calgary, Alberta, and traded on the Toronto stock exchange (symbol CAP). The company owns and operates the ColAlta Pipeline, a natural gas...

Compound A has a larger enthalpy (heat) of condensation than compound B. Which of the following statements is true? i. Heat will be released during the condensation of both substances. ii. Compound A...

Which of the following cell reactions would require the use of an inert conducting electrode? Ba(s) + 2Ag*(aq) + 2Ag(s) + Ba2*(aq) O Co(s) + 2MNO2(s) + 2NH4 (aq) Co"(aq) + Mn203(s) + 2NH3(aq) + H20)...

Why, in your opinion, is the Internet a good medium for offering sales promotions to consumers? How has social media helped to provide sales promotions to consumers?

Suppose that f(x) = 1.5x2 for 1

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) =e-x/100/1000 for x > 0 Determine the probability that (a) A component lasts more...

The probability density function of the net weight in pounds of a packaged chemical herbicide is f(x) = 2.0 for 49.75

Score! U of 1 pt P3-1 (similar to) Future values. Fill in the future values for the following table, using one of the three methods below. a. Use the future value formula, FV=PVX (1+r)? b. Use the...

Compute the discounted payback statistic for Project C if the appropriate cost of capital is 7 percent and the maximum allowable discounted payback period is three years. Time 0 1 2 3 4 5 cash flow...

Dizzyland Enterprises has been presented with an investment opportunity which will yield end-of-year cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and...