) Find the critical points ot fcx) = X² 3exIdenityincreases decreases. Find the funchion!s loca)and absolute extreme valwes.the open intervals on which F2) Do the same as above tor thedollowing two dunchions:Lux+I.luxdescribeadex+2

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Answered: ) Find the critical points t fcx) = X²3…

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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show that the x corrdinate gaurentted to exist for the mean value theorm for f(x)=1/x on the interval [a,b] with 0<a<b is C=sqrt(ab),
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6. Use the Mean Value Theorem to find all values of c in (6, 14) such that ƒ'(c) = f(b)-f(a) b-a for f(x)=√√√2x - 3 on the interval [6, 14]
Consider the function f(x) = 4/(x-6). This function has two citical numbers A< B Then A = and B . For each of the following intervals, tell whether f(x) is increasing or decreasing. (-00, A]: ? [4, B]: ? [B, 00) ? The critical number A is ? + and the critical number B is ? There are two numbers C < D where either f"(x) = 0 or f"(æ) is undefined. Then C = and D %3D Finally for each of the following intervals, tell whether f(x) is. concave up or concave down. (-00, C): ? (C, D) ? (D, 00) ?
Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = 10 x over the interval [10, 10]. In other words, find c E [10, 10] such that f(c) This function has two values, c₁ and c₂, where c₁ < C₂. 41 = 10 10-11-10) / 10 -10) / f(x)dx. - 10 - C2
2a) Use six rectangles to find estimates of each type for the aria under the given graph of f from x-0to X=12. i Lo (sample polnts are left endpoints) n.Ro(sample points are night endp0ints) i. Mc (sample points are midpoints.) b) Is Lc an wnderestimate or overestinate cf the true area? ) Is Re ano wnderestimate or overestimate of the true area? ) which of the numbers Le, Ro,or Ma gives the -best estimate? Gxplain. YA 8. 12
Let Ax) = x³ – 12x + 5. a. Find the critical values of f. b. Use your answer for a. to determine the open intervals on which f is increasing and decreasing. c. Provide the relative extrema for f. Give these as ordered pairs.
Why is 10, and 25 open intervals?
Q2.7 You have been provided with f(t) = 7t²³ (t-2) which is defined if we keep Fodd and Feven to even periodic extentions respectively then Food (0.1) = Fodd (-0.5)=_ Fodd (3)= Food (-3) =_ the function of: on [0₂2]. Feven (0.1)= Feven (-0.5)=_ Feven (3) = Feven (3) be the odd and calculate:
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) Find the critical points t fcx) = X²3 ex the open intervals on which F Idenify increases (decreases. Find the funchion!s loco" and absolute extreume valwes.