Consider f(x) = Ax2 + Bx + C with A > 0. Show that f(x) 0

Question:

Consider f(x) = Ax2 + Bx + C with A > 0. Show that f(x) ≥ 0 for all x if and only if B2 - 4AC ≤ 0.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

See More Books

Question Posted: Jun 21, 2016 09:54 AM

See More Questions

Consider the function f(x) = ax 2 + bx + c, with a 0. Explain geometrically why f has exactly one absolute extreme value on (-, ). Find the critical point to determine the value of x at which f has...
(a) Show that the set of all functions of the form f(x) = (ax2 + bx + c) ex for a, b, c, R forms a vector space. What is its dimension? (b) Show that the derivative D[f(x)] = f(x) defines an...
Consider the quadratic function f(x) = Ax 2 + Bx + C, where A, B, and C are real numbers with A 0. Show that when the Mean Value Theorem is applied to f on the interval [a, b], the number c...
Consider the no-trade input/output situation presented in the following table for countries X and Y. Assuming that free trade is allowed, develop a scenario that will benefit the citizens of...
What is a royalty fee?
Survey evidence is often introduced in court cases involving trademark violation and employment discrimination. There has been controversy, however, about whether non probability samples are...
Cloud Tech Ltd produces four types of drones, which are sold to local retail stores. The marketing department expects the following sales performance for the next year. Required Prepare a monthly...
You are the controller for Tippets Watch Company, a manufacturer of high-quality watches. The company has excess watches, which it has not been able to market through its own distribution outlets. To...
If a bank charges an interest rate of 0.6% per quarter on loans to its customers, what APR must this lender report to consumers? A bond with 10 years left to maturity currently sells for 105% of par...
Explain how managers can use a BCG Matrix to manage strategies by analyzing a corporate portfolio.
In Problems 1-3, sketch a graph of a function with the given properties. If it is impossible to graph such a function, then indicate this and justify your answer. 1. f is differentiable, has domain...
Consider f(x) = Ax3 + Bx2 + Cx + D with A > 0. Show that f has one local maximum and one local minimum if and only if B2 - 3AC > 0.
During the current year, Will Company had net sales of $176,000 and net income of $18,000. Will Companys stockholders equity was $70,000 and $80,000 at the beginning and end of the year,...
Identify the three typical categories of restructuring costs and their effects on the balance sheet and the income statement. Explain the concept of a big bath and why restructuring costs are often...
Why are extraordinary items reported separately from continuing operations in the income statement?
What is the difference between basic earnings per share and diluted earnings per share? Are potentially dilutive securities always included in the EPS computation?
Use the financial statement effects template to record the accounts and amounts for the following four transactions involving investments in marketable securities: (1) Ohlson Co. purchases 10,000...
Use the financial statement effects template (with amounts and accounts) to record the following transactions involving investments in marketable securities accounted for using the equity method: a....
Prepare journal entries for each of the following transactions: 1. Pay $700 for radio advertising for the current month. 2. Purchase supplies of $1,300 on account. 3. Provide services of $2,900 to...
2. Assume a person bends forward to lift a load "with his back" as shown in Figure P12.42a. The person's spine piv- ots mainly at the fifth lumbar vertebra, with the principal supporting force...
Consider a politician who has to determine how much effort he will exert in his re-election campaign. A: We can model such a politician as a producer of good feelings among voters. (a) Begin with a...
Public policy makers are often pressured to reduce class size in public schools in order to raise student achievement. A: One way to model the production process for student achievement is to view...
Below, we will investigate the profit maximizing choice in the two steps that first involve a strict focus on the cost side. A: Consider again (as in the previous exercise) a production process that...
Describe a time when you had to stop a client's violent or destructive behaviour. What did you do? What would you have done differently?
Analyze the integration of digital technologies, such as process simulation, computational fluid dynamics (CFD), and advanced control systems, in achieving process intensification, focusing on...
When monochromatic light of an unknown wavelength falls on a sample of copper, a minimum potential of 2.49 V is required to stop all of the ejected photoelectrons. (The work function for copper is...

Consider f(x) = Ax2 + Bx + C with A > 0. Show that f(x) 0

Question:

Step by Step Answer:

The graph of f is a parabola which opens up fX 2 Ax B 0 x B2A fx 2A Since A 0 the gra...View the full answer

Calculus

Students also viewed these Calculus questions