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(b) Consider the function f(x) = x(r+2)(6 – x). %3D i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f() > 0 for r. iii) Show that f(r) = g(x) – 4, where g(r) = -r³ + 4x² + 12x + 4. iv) Hence solve g(x) < 4 for x.

(b) Consider the function f(x) = x(r+2)(6 – x). %3D i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f() > 0 for r. iii) Show that f(r) = g(x) – 4, where g(r) = -r³ + 4x² + 12x + 4. iv) Hence solve g(x) < 4 for x.

Advanced Engineering Mathematics
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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Please answer only part iv . 

(b) Consider the function f(x) = x(x+2)(6 – x). i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f(r) 2 0 for r. iii) Show that f(r) = g(x) – 4, where g(x) = -r³ + 4.x² + 12x + 4. iv) Hence solve g(x) < 4 for r.
Transcribed Image Text:(b) Consider the function f(x) = x(x+2)(6 – x). i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f(r) 2 0 for r. iii) Show that f(r) = g(x) – 4, where g(x) = -r³ + 4.x² + 12x + 4. iv) Hence solve g(x) < 4 for r.
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