Consider the function f(1) = (r - 1)e. a) When is f(r) = 0, when is f(r) > 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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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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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