Show that the general quartic (fourth degree) polynomial f(x) x 4 ax 3 bx 2 cx d has either zero or two inflection points, and that the latter case occurs provided that b 3a 2 8 ...

Note that fx 0 exactly when This represents no real solutions when 9a 2 24b 0 which occu ...

Show that the general quartic (fourth-degree) polynomial f(x) = x 4 + ax 3 + bx 2

Question:

Show that the general quartic (fourth-degree) polynomial f(x) = x⁴ + ax³ + bx² + cx + d has either zero or two inflection points, and that the latter case occurs provided that b < 3a²/8.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Mar 05, 2019 07:13 AM

See More Questions

Find the function F that satisfies the following differential equations and initial conditions. F"(x) = 1, F'(0) = 3, F(0) = 4
Use linear approximations to estimate the following quantities. Choose a value of a that produces a small error. ln (1.05)
A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) Minimize. (b) Maximize the combined area of the circle...
How does the ERM system help with timely, effective, and democratic business decisions? A) Reporting to the presidents of each unit a faculty in a method that allows silo type decisions B) Board...
Weston Corporation had earnings per share of $1.64, depreciation expense of $310,000, and 140,000 shares outstanding. What was the operating cash flow per share? If the share price was $43, what was...
Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall...
Write a regression model relating E1y2 to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.
Albert Gaytor and his wife Allison are married and file a joint return for 2018. The Gaytors live at 12340 Cocoshell Road, Coral Gables, FL 33134. Captain Gaytor is a charter fishing boat captain but...
The following is a portion of the current asset section of the balance sheets of HiROE Co., at December 31, 2020 and 2019: 12/31/20 12/31/19 Accounts receivable, less allowance for uncollectible...
Consider the following 0x86 program: .data array DWORD 1,2,3,4,5,6,7,8,9 aravSize -(S-array)/4 ; array .code main PROC mov ecx,arraySize-1 mov esi.OFFSET array L1: mov eax. [esi] sda mov bx,2 idiv bx...
Suppose you make a deposit of $P into a savings account that earns interest at a rate of 100 r% per year. a. Show that if interest is compounded once per year, then the balance after t years is B(t)...
The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to...
JumpinJehosaPhats is a small business owned by JJ Phats as the sole proprietor. JJphats is incorporating the business. On January 1, 2012, JumpinJehosaPhats Inc. has been authorized to issue...
Determine dy/dr when 3x+4y = 3.
Problem 3. Doping a Semiconductor The following chemical scheme is used to introduce P-atoms as a dopant into a semiconductor - a silicon chip. POCI3 Cl POCI 3 vapor P P SiO2 + P(s) CVD coating Si...
The system shown in the following figure is in static equilibrium and the angle is equal to 34 degrees. Given that the mass1 is 8 kg and the coefficient of static friction between mass1 and the...
Pre-Writing step for a report for your boss on Richard Hackman's statement that using a team to complete a complex project may not be the best approach. Review your classmates' contributions to the...
For the graph of the equation x = y - 9, answer the following questions: the x- intercepts are x = Note: If there is more than one answer enter them separated by commas. the y-intercepts are y= Note:...
The molar volume of a certain solid is 161.0 cm 3 mol 1 at 1.00 atm and 350.75 K, its melting temperature. The molar volume of the liquid at this temperature and pressure is 163.3 cm 3 mol 1 . At 100...
(a) Water flows through the nozzle of a garden hose. Find an expression for m in terms of line pressure P 1 , ambient pressure P 2 , inside hose diameter D 1 , and nozzle outlet diameter D 2 . Assume...
If find the value of f'(/4). sec t - lim sec x f(x) t - x
Give several examples of how the derivative can be interpreted as a rate of change in physics, chemistry, biology, economics, or other sciences.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If f is differentiable, then d de (Vx) =...
Deacon Company is a merchandising company that is preparing a budget for the three - month period ended June 3 0 th . The following information is available Deacon Company Balance Sheet March 3 1...
Mango Company applies overhead based on direct labor costs. For the current year, Mango Company estimated total overhead costs to be $460,000, and direct labor costs to be $230,000. Actual overhead...
Which of the following do we expect to be the horizon growth rate for a company (long term growth rate- say 30-50 years)? A) Inflation B) Industry Average C) Zero D) Market Beta

Show that the general quartic (fourth-degree) polynomial f(x) = x 4 + ax 3 + bx 2

Question:

Step by Step Answer:

Note that fx 0 exactly when This represents no real solutions when 9a 2 24b 0 which occu...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions