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Consider the function f(r) = (r – 1)e. a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0? b) Compute the derivative of f. Find all stationary points, and describe when the function f is increasing and when it is decreasing. c) Compute the second derivative of f. Find all inflections points, and when the function f is concave, and when it is convex. d) Provide a sketch of the function, where you include all the important infor- mation that you have computed in point a)-c). (Here you can also write the important information besides the graph if you want).

Consider the function f(r) = (r – 1)e. a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0? b) Compute the derivative of f. Find all stationary points, and describe when the function f is increasing and when it is decreasing. c) Compute the second derivative of f. Find all inflections points, and when the function f is concave, and when it is convex. d) Provide a sketch of the function, where you include all the important infor- mation that you have computed in point a)-c). (Here you can also write the important information besides the graph if you want).

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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part  C D

Consider the function f(z) = (x – 1)e". a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0? b) Compute the derivative of f. Find all stationary points, and describe when the function f is increasing and when it is decreasing. c) Compute the second derivative of f. Find all inflections points, and when the function f is concave, and when it is convex. d) Provide a sketch of the function, where you include all the important infor- mation that you have computed in point a)-c). (Here you can also write the important information besides the graph if you want).
Transcribed Image Text:Consider the function f(z) = (x – 1)e". a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0? b) Compute the derivative of f. Find all stationary points, and describe when the function f is increasing and when it is decreasing. c) Compute the second derivative of f. Find all inflections points, and when the function f is concave, and when it is convex. d) Provide a sketch of the function, where you include all the important infor- mation that you have computed in point a)-c). (Here you can also write the important information besides the graph if you want).
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