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

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) = 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 =
-5
x2 = 3
=
3 x² + 6 x − 45
(c) Find any inflection points of f.
X =
-1
ƒ(3)
6 x + 6
(d) Evaluate ƒ at its critical points and at the endpoints of the given
interval. Identify local and global maxima and minima of f in the
interval.
f(-5) =
=
f(-10) =
=
is Choose one
is Choose one
is Choose one
Transcribed Image Text: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 = -5 x2 = 3 = 3 x² + 6 x − 45 (c) Find any inflection points of f. X = -1 ƒ(3) 6 x + 6 (d) Evaluate ƒ at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima of f in the interval. f(-5) = = f(-10) = = is Choose one is Choose one is 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
-2
2
(1, 3)
65,4)
Transcribed Image Text: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 -2 2 (1, 3) 65,4)
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