The equation of a curve is y 4x px qx where p and q are positive constants i) Show that the curve has only one stationary point when p 2 3 q ii) In the case where p 1 2 and q 6, find the set of values of x for which y is a decreasing function of x ...

i To find the stationary points on the curve we need to find where the derivative of the curve is eq ...

The equation of a curve is y = 4x + px + qx where p and q

Question:

The equation of a curve is y = 4x³ + px² + qx where p and q are positive constants.

i) Show that the curve has only one stationary point when p = 2³√q.

ii) In the case where p = 1/2 and q = −6, find
the set of values of x for which y is a
decreasing function of x.

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

Step by Step Answer:

Related Book For book-img-for-question

Complete Pure Mathematics 1 For Cambridge International AS & A Level

ISBN: 9780198427438

2nd Edition

Authors: Jean Linsky, Brian Western, James Nicholson

See More Books

Question Posted: Apr 14, 2023 11:22 AM

See More Questions

The equation of a curve is y = x 3 + px 2 , where p is a positive constant. i. Show that the origin is a stationary point on the curve and find the coordinates of the other stationary point in terms...
The equation of a curve is y = 3 + 12x 2x 2 . a. Express 3 + 12x 2x 2 in the form a 2(x + b) 2 , where a and b are constants to be found. b. Find the coordinates of the stationary point on the...
The number e is readily calculated to as many digits as desired using the rapidly converging series e = 1 + 1 + 1 / 2! + 1 / 3! + 1 / 4! + ... This series can also be used to show that e is...
A car costs 12,000. It will be kept for three years, and then sold for 3,000. Calculate the depreciation for each year using (a) the reducing balance method, using a depreciation rate of 35 per cent,...
TechPro offers instructional courses in e-commerce website design. The company holds classes in a building that it owns. Classify each of TechPros costs below as (a) Variable or fixed (b) Direct or...
A long cart moves at relativistic speed v. Sand is dropped into the cart at a rate dm/dt = in the ground frame. Assume that you stand on the ground next to where the sand falls in, and you push on...
Carry out a pre-posterior analysis and find the expected value of perfect information (EVPI).
Castner Corporation is considering implementation of a JIT inventory system. The companys industrial engineer recently conducted a study to determine the average number of days spent in each activity...
Analysis 1. Make a graph of height vs range using all 8 data points. Remember to include titles 2. Determine the "muzzle" velocity, or v, of the launcher using your most consistent range result. Show...
Write a query to display the patron ID, book number, and days kept for each checkout. Days Kept is the difference from the date on which the book is returned to the date it was checked out. Sort the...
The diagram shows a semicircle on top of a rectangle. The perimeter of the shape is 20 cm. Find the maximum area of the rectangle. rcm hcm
The equation of a curve is y = 5x + 3/x, i) Obtain an expression for dy/dx ii) A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.04 units per...
Using the Frequently Asked Questions segment of www.securitieslaw.com answer the following questions: 1. What duties are owed by stockbrokers and brokerage firms to customers? 2. How does a customer...
Obtain the 1s and 2s complements of the following unsigned binary numbers: 10011100, 10011101, 10101000, 00000000, and 10000000.
The beds below an angular unconformity have an attitude of 334, 74W, and those above 030E, 54NW. What was the attitude of the older beds while the younger beds were being deposited?
Explain clearly why both the cache memory concept and the virtual memory concept would be ineffective if locality of reference of memory-addressing patterns did not hold.
Repeat Problem 4-27 with D lip- lops using a Gray- code assignment. Problem 4-27: A sequential circuit has two lip- lops A and B, one input X, and one output Y. The state diagram is shown in Figure...
Four programs are concurrently executing in a multitasking computer with virtual memory pages having 4 KB. Each page table entry is 32 bits. What is the minimum numbers of bytes of main memory...
N atoms can have a wide range of oxidation numbers. Assign oxidation numbers for the N atom in each compound, all of which are known compounds. a. N2O5 b. N2O4 c. NO2 d. NO e. N2H4 f. NH3
Use the graphs of f and g to graph h(x) = (f + g) (x). To print an enlarged copy of the graph, go to MathGraphs.com. 1. 2. y 24 8. 2. -2 -2 4 6
Registered Retirement Savings Plan are retirement plans that defer taxes. Many Canadians rely on these plans for their retirement. To measure how these are doing, a random sample of 60-yearold...
How much do American families spend on entertainment each month. A survey was conducted and the amounts spent on entertainment in the previous month were recorded. Assuming that the population...
The rising cost of electricity is a concern for homeowners. An economist wanted to determine how much electricity has increased over the past 5 years. A survey was conducted with the percentage...
Assume Video is a valid concrete class with a default constructor. Examine the following code and fill in the blanks assuming no other code is executed. ONLY put a number in the blank, or the...
What was observed in the magnetic field after the addition of another magnetic field in the Helmholtz set-up? Based on your model, what happens to the magnetic field as the distance between the two...
What quality assurance protocols do you employ to test and validate data integrity in software applications and databases ?

The equation of a curve is y = 4x + px + qx where p and q

Question:

Step by Step Answer:

i To find the stationary points on the curve we need to find where the derivative of the curve is eq...View the full answer

Complete Pure Mathematics 1 For Cambridge International AS & A Level

Students also viewed these Mathematics questions