a. Find the slope of the folium of Descartes x 3 + y 3 - 9xy =

Question:

a. Find the slope of the folium of Descartes x³ + y³ - 9xy = 0 at the points (4, 2) and (2, 4).

b. At what point other than the origin does the folium have a horizontal tangent?

c. Find the coordinates of the point A in Figure 3.28 where the folium has a vertical tangent.

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

Step by Step Answer:

Related Book For book-img-for-question

Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

See More Books

Question Posted: Apr 18, 2023 12:48 AM

See More Questions

The graph of x 3 + y 3 = 9xy is the folium of Descartes shown in Fig. 4. (a) Find dy/dx by implicit differentiation. (b) Find the slope of the curve at (2, 4). x + y + 1 = 0 Asymptote y -X x + y =...
a. Find all points where the following curves have vertical and horizontal tangent lines. b. Find the slope of the lines tangent to the curve at the origin (when relevant). c. Sketch the curve and...
Benny sells an apartment building. His adjusted basis for regular income tax purposes is $450,000, and it is $475,000 for AMT purposes. He receives $700,000 from the sale. a. Calculate Bennys gain...
Many universities now offer Web-based courses in lieu of traditional classes. These courses often contain lecture notes, linkages to videos and other documents, and online testing capabilities. How...
A group of medical professionals is considering constructing a private clinic. If patient demand for the clinic is high, the physicians could realize a net profit of $100,000. If the demand is low,...
Comment on the following: An information system is a product.
Recall the Innis Investments problem. Letting S = units purchased in the stock fund M = units purchased in the money market fund Leads to the following formulation: Min8S + 3M s.t. 50S + 100M ...
What are the key considerations in designing a network organizational structure that optimizes knowledge sharing and innovation across decentralized nodes while maintaining strategic alignment and...
There is a parcel of land next to the Playful Paws, Inc. building. Ellen, the owner of this property, approached John to discuss the idea of selling it to him. John is interested. Ellen knows that...
Find the derivatives of the function. sec Vetan r = sec 1 0
Find the two points where the curve x 2 + xy + y 2 = 7 crosses the x-axis, and show that the tangents to the curve at these points are parallel. What is the common slope of these tangents?
In a detergent making process, 1400 gal/hr of water flows through a 2-inch pipe system as follows: Exit from pump, 2 ft vertical, open gate valve, 14 ft vertical, 90 bend, 12 ft horizontal, open...
The 5 kg crank arm (OA) is rotating at a constant speed of 100 rpm. The uniform piston rod AB has a mass of 6.3 kg and at 0 = 67 the piston is subject to a piston chamber force of P = 800 N. If the...
4) Find the solution of the differential equation. dx dt + 9x + 12 sin 3t = : 0, t 0 with x = 1, dx dt = 2 at t = 0. [10 marks]
3. Here is an example with some data. Make a plot of the data and fit a curve (line). a Sandwich Hamburger Cheeseburger ax + b[x = xx Xiyi Quarter Pounder Quarter Pounder with Cheese Big Mac Arch...
A thermostat has a resistance of 2.5 kohm at the ice point and 0.12 kohm at 50C. Calculate the range of resistance to be measured if the instrument is to measure temperature in the range of 30C to...
Air at 200 kPa and 400 K is contained in a 10 m insulated tank. The 80 kg weight is lowered by 2 m. The final pressure of air in the tank would be kJ kgK' kPa kJ [c=0.718- R = 0.287- kgk 9= 10 m/s]...
What are the objectives of query processing?
Avatar Financials, Inc., located on Madison Avenue, New York City, is a company that provides financial advice to individuals and small- to mid-sized businesses. Its primary operations are in wealth...
In problem, sin and cos are given. Find the exact value of each of the four remaining trigonometric functions. 4 sin 0 5' 5 cos e in
In problem, sin and cos are given. Find the exact value of each of the four remaining trigonometric functions. V5 sin 0 cos e 5. 5.
In problem, sin and cos are given. Find the exact value of each of the four remaining trigonometric functions. V5 2V5 5 sin 0 cos e
Given the normalized wavefunction for a particle on a 2D ring w() expectation value of angular momentum from the operator = e 2 = = -i im, o ' where 02, evaluate the
10. (10 points) Consider the following circuit: Vi RI V2 R2 R3 ww The two batteries V and V2 (9 V) are connected to three resistors of values R R2 = 4.0 and R3 = 4.52. What is the current through R3?...
At a certain time instant, the 2 = a ^ + b m .76 c + d m/s ++ || ||(^) || 1 d dt dn) dt vector (t) has At this sane instant of time, Solve below. d 8' (alt)(t)) dt d (a(t). (t)) dt dt (A) (A)) a(t)...

a. Find the slope of the folium of Descartes x 3 + y 3 - 9xy =

Question:

5 r³+y3-9xy=0 (Xo-V₁) [(xo-Y₂) xo y = f(x) A y=f₂(x) 5 (xp- Y3) y=f(x) X

Step by Step Answer:

ANSWER a To find the slope of the folium of Descartes at the points 4 2 and 2 4 we need to first fin...View the full answer

Thomas Calculus Early Transcendentals

Students also viewed these Mathematics questions