3. Let f(x) = c.(x-4)+2 if 0 ≤x≤4 if x > 4 where c denotes a real constant. (a) Show that lim f(x) = lim f (x) and that fe is continuous at x = 4 for any real c. x->4+ X-4 (b) Sketch the curves y = f(x) on separate graphs for c=0, c=1, and c= -1. (c) Determine the unique value of c for which fe is differentiable at x = 4, i.e., find c so that (f)+ (4) = (f)'_ (4).

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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3. Let f(x) =
c.(x-4)+2
if 0 ≤x≤4
if x > 4
where c denotes a real constant.
(a) Show that lim f(x) = lim f (x) and that fe is continuous at x = 4 for any real c.
x->4+
X-4
(b) Sketch the curves y = f(x) on separate graphs for c=0, c=1, and c= -1.
(c) Determine the unique value of c for which fe is differentiable at x = 4,
i.e., find c so that (f)+ (4) = (f)'_ (4).
Transcribed Image Text:3. Let f(x) = c.(x-4)+2 if 0 ≤x≤4 if x > 4 where c denotes a real constant. (a) Show that lim f(x) = lim f (x) and that fe is continuous at x = 4 for any real c. x->4+ X-4 (b) Sketch the curves y = f(x) on separate graphs for c=0, c=1, and c= -1. (c) Determine the unique value of c for which fe is differentiable at x = 4, i.e., find c so that (f)+ (4) = (f)'_ (4).
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