Given the function f(x) = x³ + 3x² - 45x+8 over the interval−10 ≤ x ≤ 5, answer the following questions.(a) Find f'(x) and f"(x).ƒ'(x)==f"(x)(b) Find the critical points of f.x1 =-5x2 = 3=3 x² + 6 x − 45(c) Find any inflection points of f.X =-1ƒ(3)6 x + 6(d) Evaluate ƒ at its critical points and at the endpoints of the giveninterval. Identify local and global maxima and minima of f in theinterval.f(-5) ==f(-10) ==is Choose oneis Choose oneis Choose one f(-10) =ƒ(5)=(-10, 1)is Choose one(e) Move the points on the grid to sketch the function f.(-6, 1)is Choose one-22(1, 3)65,4)

Answered: Image /qna-images/answer/17ccf472-d2b6-4c57-b64b-e2bd4f6ff7b0.jpg

Answered: Given the function f(x) -10 ≤ x ≤ 5,…

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) -10 ≤ x ≤ 5, answer the following questions. = a) Find f'(x) and ƒ"(x). f'(x) = 3 x² + 6 x − 45 x³ + 3x² - 45x + 8 over the interval f"(x) = 6 x + 6 b) Find the critical points of f. x1 = -5 x2 = 3 c) Find any inflection points of f. x = -1