Use the given graph of the function on the interval [0, 8] to answer the following questions.Note: If there are no such values, enter "none".Note: A filled-in point indicates that it is included on the graph, an open point is NOT included.1. For what values of a does the function f have a local (relative) maximum on (0,8)?Answer (separate by commas): x =2. For what values of a does the function f have a local (relative) minimum on (0,8)?Answer (separate by commas): * =3. Find the absolute maximum value for the function f on the interval [0, 8].Answer:4. Find the absolute minimum value for the function f on the interval [0, 8].Answer: -1110-1488

1. For x= 3, the function f(x) has a local maximum in the interval (0,8) 2. For x=2 , the function…

Answered: 1. For what values of a does the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the function f(x) = - (x+4)3, which of the following statement talks about its relative and absolute extrema at interval [-4, – 3]? (A Absolute maximum at the point (-4, 0) ; absolute minimum point at the point (-3, – 1) : no relative extrema (B There are no relative and absolute extrema. C) Absolute and relative maximum at the point (-4, 0) ; absolute and relative minimum at the point (- 3, – 1) D) Relative maximum at the point (-4, 0) ; relative minimum at the point (-3, – 1) ; no absolute extrema
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1.) Given the function in the graph, answer the following questions. g(x) = x³ - 3x g(x) a.) What are the domain and range of the function? Write your answer in interval notation. b.) State the intervals on which the function increasing or decreasing. c.) Identify all relative extrema of g(x). d.) Find the average rate-of-change from x = -1 to x = 1.
please find the correct answer
Find the maximum and minimum values of the function f(x, y) = 2x² + 3y² - 4x-5 on the domain 2 + y² 256. The maximum value of f(x,y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x, y) is: List points where the function attains its minimum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7).
A.) What are the relative minimum and relative maximum values over the interval [-3,2] for the function shown in the graph? B.) At what intervals is the entire function increasing? C.) At what intervals is the entire function decreasing?
Given two points A(1, 8) and B(6, 14). Find the point C on the x-axis so that the total distance AC + BC is a Minimum Distance. {Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.} Give at least 3 decimal places. Minimum Total Distance of occurs when C = ,0) DO NOT USE CALCULUS.
9. Find the coordinates of the cusp of this piecewise function illustrating a texting plan: (35 when x ≤ 100 f(x)= 35+0.35(x-100) when x > 100 A. (100, 35) B. (35, 100) C. (0.35, 100) D. (100, 0.35)
, (2,00) 3x3 +3x²+ 4. The below graph shows a function f(z) on the y-axis. Write the (F,y) coordi- nates for the absolute maximum and minimum of f on the domain (0,7) (2) wjm x=3 x2 y=-47,5 g=-16 O ·N 3 5 6. (b) g reaches a local minimum, -80- . Now assume the above graph shows a derivative g'(x) on the y-axis. For the function g(x) (not shown) with domain (∞, ∞), identify the x-values where: #f (a) g reaches a local maximum
Find and sketch the domain for the function. f(x,y) = / (x? - 9) (,² -4) Find the domain of the function. Express the domain so that coefficients have no common factors other than 1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is all points (x,y) satisfying >0. B. The domain is all points (x,y) satisfying #0. OC. The domain is all points (x,y) satisfying 20. O D. The domain is the entire xy-plane. Choose the correct sketch below. The domain is shaded in yellow. O A. O B. C. D. Ay 40- Ay 10 Ay 10- Ay 10 -TO 10 10
Consider the function f(x) = -x2 + 10x + 100. The minimum value of the function in the interval [5, 10] is -
show all formulas and all steps of justification. Provide proper units

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