The equation of a curve is y 3 12xy + 16 = 0. a. Show that

Question:

The equation of a curve is y³− 12xy + 16 = 0.
a. Show that the curve has no stationary points.
b. Find the coordinates of the point on the curve where the tangent is parallel to the y-axis.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Mar 18, 2023 07:08 AM

See More Questions

The equation of a curve is y 2 4xy x 2 = 20. a. Find the coordinates of the two points on the curve where x = 4. b. Show that at one of these points the tangent to the curve is parallel to the...
The equation of a curve is 5x 2 + 2xy + 2y 2 = 45. a. Given that there are two points on the curve where the tangent is parallel to the x-axis, show by differentiation that, at these points, y = 5x....
The equation of a curve is ln(xy) y 3 = 1. i. Show that ii. Find the coordinates of the point where the tangent to the curve is parallel to the y-axis, giving each coordinate correct to 3...
Compare to traditional organizational development approaches. To get back on track and find a way to function more smoothly, should this taskforce use an Appreciative Inquiry approach or a more...
Use the binomial table to find the following probabilities: a. P ( x = 1), where n = 9, p = .2 b. P (x = 4), where n = 20, p = .35 c. P (3 < x < 5), where n = 15, p = .5 d. P(x > 2), where n = 10, p...
A 0.550 kg ball falls directly down onto concrete, hitting it with a speed of 12.0 m/s and rebounding directly upward with a speed of 3.00 m/s. Extend a y axis upward. In unit-vector notation, what...
You are faced with making a decision on a large capital investment proposal. The capital investment amount is $\$ 640,000$. Estimated annual revenue at the end of each year in the eight-year study...
Leah Sanchez is concerned that if she orders too few calendars, customers disappointment in not finding a calendar might drive them to shop elsewhere, resulting in more of a loss over the long term...
MyBnB started a home rental company on January 1. As of November 30, MyBnB reported the following balances. The company does not yet have a balance in Retained Earnings because this is its first year...
The line 2x 2y = 5 intersects the curve 2x 2 y x 2 26y 35 = 0 at three points a. Find the x-coordinates of the points of intersection. b. Find the gradient of the curve at each of the points of...
a. By writing sec x as 1/cosx, find d/dx(secx). b. By writing cosec x as 1/sin x, find d/dx(cosecx). c. By writing cot x as cosx/sinx , find d/dx (cotx).
If the minimum wage were eliminated, the employment of marginal workers would _________. a) rise a lot b) rise a little c) stay exactly the same d) fall a little e) fall a lot f) fall by an...
Evaluate Nike's specific initiatives in the metaverse. What are the pros and cons of each? How can you help achieve company objectives? 2.How should these initiatives be organized, and which should...
Discuss your informed thoughts on how this age group's developmental stage/tasks can impact their motivation, group dynamics, communication patterns, and group cohesion.
Describe the Control Scope process, its inputs, tools, techniques and outputs. explain Control scope management its inputs, tools, techniques and outputs.
Please express in one paragraph why you feel there are benefits to Using an Outline for your Public Speaking?
Find the Strongly Connected Components usingTarjan's SCC Algorithm S h b g.
An uninsulated cylinder fitted with a piston contains air at 500 kPa, 200C, at which point the volume is 10 L. The external force on the piston is now varied in such a manner that the air expands to...
Show that every group G with identity e and such that x * x = e for all x G is abelian.
The straight line y = x + 1 intersects the curve x 2 y = 5 at the points A and B. Given that A lies below the x-axis and the point P lies on AB such that AP : PB = 4 : 1, find the coordinates of P.
Prove that any quadratic that has its vertex at ( p, q) has an equation of the form y = ax 2 2apx + ap 2 + q for some non-zero real number a.
Prove that x 2 + kx + 2 = 0 has real roots if k 2 2. For which other values of k does the equation have real roots?
Remo Company and Angelo Incorporated are separate companies that operate in the same industry. Following are variable costing income statements for the two companies showing their different cost...
What are factoids and can you give an example of how they are used today?
Kayak Company budgeted the following cash receipts (excluding cash receipts from loans received) and cash payments (excluding cash payments for loan principal and interest payments) for the first...

The equation of a curve is y 3 12xy + 16 = 0. a. Show that

Question:

Step by Step Answer:

a To find stationary points we need to find where the derivative of y with respect to x is equal to ...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions