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14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing and that its graph is concave down.

14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing and that its graph is concave down.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4). a) Consider the function f (x) = x – 2e¬* + 1 for x 2 0. i) Show that the function is increasing and that its graph is concave down. ii) Examine f (x) as x → ∞ and sketch the graph of y = f(x). Clearly show the equations of any asymptotes. iii) On the same diagram, sketch the graph of the inverse function y = f-²(x). %3D iv) Find the x value of the point of intersection of the two curves.
Transcribed Image Text:4). a) Consider the function f (x) = x – 2e¬* + 1 for x 2 0. i) Show that the function is increasing and that its graph is concave down. ii) Examine f (x) as x → ∞ and sketch the graph of y = f(x). Clearly show the equations of any asymptotes. iii) On the same diagram, sketch the graph of the inverse function y = f-²(x). %3D iv) Find the x value of the point of intersection of the two curves.
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