Use the equation to establish the following test. Let have continuous first and second derivatives and
Question:
Use the equation
to establish the following test. Let ƒ have continuous first and second derivatives and suppose that ƒ′(a) = 0. Then
a. ƒ has a local maximum at a if ƒ″ ≤ 0 throughout an interval whose interior contains a;
b. ƒ has a local minimum at a if ƒ″ ≥ 0 throughout an interval whose interior contains a.
Transcribed Image Text:
f(x) = f(a) + f'(a)(x - a) + f" (c₂) 2 -(x − a)²
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (9 reviews)
To use the given equation to establish this test we can apply it to the functi...View the full answer
Answered By
Rodrigo Louie Rey
I started tutoring in college and have been doing it for about eight years now. I enjoy it because I love to help others learn and expand their understanding of the world. I thoroughly enjoy the "ah-ha" moments that my students have. Interests I enjoy hiking, kayaking, and spending time with my family and friends. Ideal Study Location I prefer to tutor in a quiet place so that my students can focus on what they are learning.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
Suppose f has continuous first and second derivatives at a. a. Show that if f has a local maximum at a, then the Taylor polynomial p 2 centered at a also has a local maximum at a. b. Show that if f...
-
Let I be an open interval, f : I R, and c l. The function f is said to have a local maximum at c if and only if there is a > 0 such that f(c) > f(x) holds for all |x - c| a) If f has a local...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Growth Strategy A. Organic Growth This section describes how JB Hi-Fi Australia can take advantage of various organic growth strategies, including new product development, market development and...
-
Zoe Ltd. has the following SFP at December 31, 20X5: Zoe Ltd. Statement of Financial Position December 31, 20X5 On December 31, 20X5, Halifax Ltd. bought 70% of the outstanding shares of Zoe Ltd. and...
-
A completed worksheet for The King Group is shown on the bottom of these two pages. INSTRUCTIONS 1. Record balances as of December 31, 2016, in the ledger accounts. 2. Journalize (use 3 as the page...
-
What does argv provide to our program?
-
Autotech Manufacturing is engaged in the production of replacement parts for automobiles. One plant specializes in the production of two parts: Part 127 and Part 234. Part 127 produced the highest...
-
What is the net electric charge of this object? Note for advanced students: you can assume charge is measured in any convenient units, e.g. coulombs or units of e. Write down only the number part of...
-
Heather Adams, production manager for a Colorado exercise equipment manufacturer, needs to schedule an order for 50 UltimaSteppers, which are to be shipped in week 8. Subscripts indicate quantity...
-
Use Taylors formula with a = 0 and n = 3 to find the standard cubic approximation of (x) = 1/(1 - x) at x = 0. Give an upper bound for the magnitude of the error in the approximation when |x| 0.1.
-
Use Theorem 20 to find the series interval of convergence and, within this interval, the sum of the series as a function of x. M8 n=0 1 +1 3 n
-
Use Figure 15.23(a) on page 669 to explain why Model I without hospital 14 has made the original hospital 17 considerably less influential and the original hospital 16 only slightly more influential.
-
If BZ Engineers provides its two employees with $460 worth of protective clothing (each), for no cost to each employee, for use only at work, during the FBT year ended 31 March 2023, what would the...
-
Suppose that we have two hosts. Host A sends a TCP segment ( ( Seq = 4 3 , ACK = 1 0 3 ) , which host B replies with a TCP segment ( ( Seq = 1 0 3 , ACK = 5 7 ) . What is the size of the rst TCP...
-
4) Convert the following binary values from 4 bit numbers to 7 bit values a) 2s complement value: 0101 b) 2s complement value: 1010 c) Unsigned binary value: 0101 d) Unsigned binary value: 1010 e)...
-
A company accrued salary expense of $2,000. How would this be shown on the Statement of Cash Flows? A company accrued salary expense of $2,000. How would this be shown on the Statement of Cash Flows?
-
Alice received property as a beneficiary of her father's estate when he died during the most recent tax year. what would be the starting date for the holding period of property that alice acquired?
-
MRT, a calendar year corporation, placed the following assets in service this year: a. Compute MRTs MACRS depreciation with respect to the assets placed in service this year. Assume MRT does not...
-
Write the general quadratic equation y2 - 8y - 4x + 28 = 0 in standard form. Determine the vertex, focus, and directrix of the parabola defined by this equation. Sketch a graph.
-
Find (a) the curl and (b) the divergence of the vector field. F(x, y, z) = (e x sin y, e y sin z , e z sin x)
-
Find (a) the curl and (b) the divergence of the vector field. F(x, y, z) = (arctan(xy), arctan(yz), arctan(zx))
-
The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is indepen- dent of z and its z-component is 0.) (a) Is div F positive, negative, or...
-
Linux Lingo: You may have noticed by now that Linux has a lot of unusual naming conventions. Some processes and features have names inspired by historical or literary context, while some are just...
-
What are multi user systems? b) Why are they successful? 2) Concerning Linux a) What programming language is Linux written in? b) How did this language influence the success of Linux?
-
Suppose that 4% of desktop computers run the Linux operating system (L). Suppose 2 computers are randomly selected (assume independence). (a) Find the probability that neither computer is running...
Study smarter with the SolutionInn App