Question: If a rectangle has its base on the -axis and two vertices on the curve y = ex2, show that the rectangle has the largest

If a rectangle has its base on the -axis and two vertices on the curve y = e–x2, show that the rectangle has the largest possible area when the two vertices are at the points of inflection of the curve.

Step by Step Solution

★★★★★

3.38 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let y fx e The area of the rectangle under the curve from to x is Ax 2xe where x 0 We m... 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)

M-C-D (593).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y = 16 - x 2 . What are the dimensions of the rectangle with the maximum area? What is that area?

A rectangle is constructed with its base on the diameter of a semicircle with radius 5 and its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area?

1. A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1x2. What are the dimensions of such a rectangle with the greatest possible area? Width=? Height=? 2....

help me with this ASAP please show short solution no need to explain or anything solve ASAP 3. Find the largest possible area of a rectangle inscribed in the region bounded by the half- hyperbola y2...

9. What is the maximum area of a triangle having 15 cm as the sum of its base and height? (Marks /3) COMMUNICATION: (Marks /8) 10. Complete the square to express each relation in vertex form. Then...

please show work, thank you. The base of a rectangle lies along the x-axis, and the upper two vertices are on the curve defined by y = 3 - x2. See the diagram below for an example: Find the dimension...

Please answer thank you 2ND PERFORMANCE TASKS: PRECALCULUS First Semester S.Y. 2021-2022 INSTRUCTIONS: Read and analyze each problem carefully and solve for what is asked. Show complete solution on a...

270 Chapter 4 Applications of Derivatives c. What is the largest area the rectangle can have, and what are its dimensions? 12. Find the volume of the largest right circular cone that can be in- X...

*solve the attached4 questions. 15. Let /(x) =e-2' (a) Find any horizontal and vertical asymptotes of f(r). (b) Find the intervals where f(7) is increasing and the intervals where f (7) is...

SHOW WORK ON ALL FREE RESPONSE. QUESTION 1 1 Given: , C is the midpoint of both and . Prove: Complete the proof below by choosing the correct reasons for line numbers 3 and 7. Statement Reason Given...

For country 1, SL depreciation is $20,000 per year. Determine the (a) CFAT series (b) PW of depreciation, taxes, and CFAT series. Open Access, Inc. is an international provider of computer network...

21. -, a. Cunto es tu camiseta favorita? -Quiero llevar la camiseta azul. b. Cules c. Cul d. Qu 22. -2. quieres correr? -Quiero correr alrededor (around) del Lago de Poway (Poway Lake). a. Cmo c. Por...

Can you think of an industry (or product) with near infinite elasticity of supply in the short term? That is, what is an industry that could increase Qs almost without limit in response to an...

Knowing that crank AB rotates about point A with a constant angular velocity of 900 rpm clockwise, determine the acceleration of the piston P when = 60?. 6.

Fio Barellis was discussing summer employment with Sara Rida, president of Xanadu Construction Service: Sara: Im glad that youre thinking about joining us for the summer. We could certainly use the...

You drop a ball from a height of 2.0m, and it bounces back to a height of 1.5m. (a) What fraction of its initial energy is lost during the bounce? (b) What is the balls speed just as it leaves the...

Brushy Mountain Mining Companys ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the companys earnings and...

Several years ago, Rolen Riders issued preferred stock with a stated annual dividend of 10% of its $100 par value. Preferred stock of this type currently yields 8%. Assume dividends are paid...

Fake products make up 5 to 7 percent of world trade and include everything from counterfeit electronics, medications, pirated DVDs, and computer software to toys, cosmetics, and household products....

Use a graphing device to draw the solid enclosed by the paraboloids z = x 2 + y 2 and z = 5 - x 2 - y 2 .

Sketch the solid whose volume is given by the integral and evaluate the integral. 7/2 r dz dr de J-m/2 Jo Jo

Sketch the solid whose volume is given by the integral and evaluate the integral. r dz de dr 1o Jo LII

Six people were asked to determine the amount of money they were carrying, to the nearest dollar. The results are shown below. Complete parts a and b. $32, $62, $14, $27, $4, $59 0 a) Determine the...

ive filled out what i can... im stuck. Raleigh Department Store converted from the conventional retail method to the LIFO retail method on January 1, 2014, and is now considering converting to the...

Suppose that in a claw game at an arcade, there is a collection of toys that have the following characteristics: 2/5 are red; 3/5 are waterproof; 1/2 are cool. (When we write that 2/5 are red, this...