Let P(a, a 2 ), a > 0, be any point on the part of the parabola

Question:

Let P(a, a²), a > 0, be any point on the part of the parabola y = x² in the first quadrant, and let R be the region bounded by the parabola and the normal line through P. (See the figure.) Show that the area of R is smallest when a = 1/2 .

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

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

See More Books

Question Posted: Jan 15, 2021 05:39 AM

See More Questions

Suppose R is the region bounded by y = f (x) and y = g(x) on the interval [a, b], where f(x) g(x). a. Show that if R is revolved about the vertical line x = x 0 , where x 0 < a, then by the shell...
Suppose R is the region bounded by y = f(x) and y = g(x) on the interval [a, b], where f(x) g(x) 0. a. Show that if R is revolved about the horizontal line y = y 0 that lies below R, then by the...
If v lies in the first quadrant and makes an angle /3 with the positive x-axis and |v| = 4, find v in component form.
A gaseous mixture consists of 80.0 mole percent N2 and 20.0 mole percent O2 (the approximate composition of air). Suppose water is saturated with the gas mixture at 25C and 1.00 atm total pressure,...
Identify five stakeholders of the business community, and give reasons as to why they would have an interest.
Private insurance provides numerous coverages that can be used to meet specific loss situations. For each of the following situations, identify a private insurance coverage that would provide the...
Panther Racing, LLC, is involved in competitive racing, including the development, maintenance, and operation of a racing team in the IndyCar series. Beginning in 2008, the National Guard annually...
Jalapenos! is based in Pleasant Hill, California. The merchandising company has three divisions: Clothing, Food, and Spices. The Clothing division has two main product lines: T-shirts and...
(2) To solve a nonlinear BVP Fi(yj) = 0 using Newton's method, we make a guess for y; and then iterate until the norm of the residual ||Fi|| e. Set (k+1) yj = (k) = y; " + Ayj, k = 0, 1, 2, ... where...
Garys TV had the following accounts and amounts in its financial statements on December 31, 2022. Assume that all balance sheet items reflect account balances at December 31, 2022, and that all...
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the...
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x 1, y = 0, x = 5;...
State the hypotheses used in the ANOVA test.
When an indorsement is forged or unauthorized, who bears the burden of loss?
The central finance function is one of the central corporate functions of a conglomerate. Do you foresee a trend towards the formation of a global swapping bank account? What are the pros and cons of...
Mukisa makes out a check Pay to the order of Adroa. Adroa indorses the check on the back by signing his name. Before Adroa signed his name, the check was a. bearer paper. b. order paper. c. both a...
An unauthorized signature usually binds the person whose name is forged. (True/False)
The rights and duties of a bank and its customers are partly contractual.(TRUE/FALSE)
Suppose is a general quadratic form on ?. . whose coefficient matrix A is not necessarily symmetric. Prove that r/(x) = xTKx. where K = 1/2 (A + AT) lisa symmetric matrix. Therefore, we do not lose...
Why did management adopt the new plan even though it provides a smaller expected number of exposures than the original plan recommended by the original linear programming model?
Sketch the graph of a function that is continuous on an open interval (a, b) but has neither an absolute maximum nor an absolute minimum value on (a, b).
Explain how to apply the Second Derivative Test.
Give the formula for Newtons method for the function f(x) = x 2 - 5.
5. On a warm day (32C) you hear an ambulance behind you, so you pull over to the side of the road and stop. You happen to have a microphone with you and notice that the frequency of the siren changes...
Zhdanov, Inc. forecasts that its free cash flow in the coming year, i.e., at t-1, will be -$15 million (negative), but its FCF at t-2 will be $30 million. After Year 2, FCF is expected to grow at a...
4) Protons moving horizontally at a speed of 100 km/s enter into a region with uniform electric field that extends a distance d = 3.00 cm, as shown below. The electric field is directed vertically,...

Let P(a, a 2 ), a > 0, be any point on the part of the parabola

Question:

y A (P

Step by Step Answer:

From the solution to Problem 11 in Problems Plus following Chapter ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions