Sketch the graph of ONE function that satisfies ALL of the follow- ing conditions. Label ALL important features: local extrema, inflection points, asymptotes etc. (a) ƒ(0) = 0, ƒ'(−2) = f'(1) = f'(9) = 0 lim f(x) = x→6 (b) lim f(x) = 0, x →∞ (c) f'(x) < 0 on (-∞, —2) U(1, 6) U(9, ∞) (d) f'(x) > 0 on (−2, 1) U(6, 9) (e) ƒ"(x) < 0 on (0,6) U(6, 12) (f) f'(x) > 0 on (-∞,0) U(12, ∞) =18

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Sketch the graph of ONE function that satisfies ALL of the follow-
ing conditions. Label ALL important features: local extrema, inflection
points, asymptotes etc.
(a) ƒ(0) = 0, ƒ'(−2) = ƒ'(1) = f'(9) = 0
(b) lim f(x) = 0,
lim f(x) =
x →∞
x 6
(c) f'(x) <0 on (-∞, -2) U(1,6) U(9, ∞)
(d) f'(x) > 0 on (-2, 1) (6,9)
(e) ƒ"(x) < 0 on (0,6) U(6, 12)
(f) ƒ"(x) > 0 on (-∞,0) U(12, ∞)
=10
Transcribed Image Text:Sketch the graph of ONE function that satisfies ALL of the follow- ing conditions. Label ALL important features: local extrema, inflection points, asymptotes etc. (a) ƒ(0) = 0, ƒ'(−2) = ƒ'(1) = f'(9) = 0 (b) lim f(x) = 0, lim f(x) = x →∞ x 6 (c) f'(x) <0 on (-∞, -2) U(1,6) U(9, ∞) (d) f'(x) > 0 on (-2, 1) (6,9) (e) ƒ"(x) < 0 on (0,6) U(6, 12) (f) ƒ"(x) > 0 on (-∞,0) U(12, ∞) =10
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