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Use calculus to show that the function, f (x) = x³ + 3x – 6, has exactly three zeros (where f(x) = 0) and that one zero is in (1, 2). i) Sketch the graph of f(x). Determine whether f(x) is ii) even or odd or neither, ii) decreasing or increasing or neither.

Use calculus to show that the function, f (x) = x³ + 3x – 6, has exactly three zeros (where f(x) = 0) and that one zero is in (1, 2). i) Sketch the graph of f(x). Determine whether f(x) is ii) even or odd or neither, ii) decreasing or increasing or neither.

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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Use calculus to show that the function, f(x) = x³ + 3x – 6, has exactly three zeros (where f(x) = 0) and that one zero is in (1, 2). i) Sketch the graph of f(x). Determine whether f(x) is ii) even or odd or neither; iii) decreasing or increasing or neither.
Transcribed Image Text:Use calculus to show that the function, f(x) = x³ + 3x – 6, has exactly three zeros (where f(x) = 0) and that one zero is in (1, 2). i) Sketch the graph of f(x). Determine whether f(x) is ii) even or odd or neither; iii) decreasing or increasing or neither.
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