Consider the function x²+2x-1 if x ≤ -1 f(x) = 3/8x if 1< x < 1 2x+4 if x 1 3 -1, we compute (a) To determine whether f is differentiable at x=-1 lim h→0+ 2/3 f(−1 + h) − f(−1) h - = lim h→0+ lim h→0- 0 ƒ(−1 + h) − f(−1) h = lim h→0- (b) To determine whether f is differentiable at x = 0), we compute lim h→0 f(h) — f(0) h lim 0+4 (c) To determine whether f is differentiable at x = 1, we compute lim h→0+ lim h→0- ƒ(1+ h) − f(1) h f(1+h) − f(1) h - = lim 2h/3/h h→0+ = lim h→0- (d) Classify the differentiability of f at each of the points. f is differentiable at x=a 1. x = 1 f has a vertical tangent line at x=a 2. x = 0 f has a cusp at x=a 3. x=-1 = 2/3 = 2/3
Consider the function x²+2x-1 if x ≤ -1 f(x) = 3/8x if 1< x < 1 2x+4 if x 1 3 -1, we compute (a) To determine whether f is differentiable at x=-1 lim h→0+ 2/3 f(−1 + h) − f(−1) h - = lim h→0+ lim h→0- 0 ƒ(−1 + h) − f(−1) h = lim h→0- (b) To determine whether f is differentiable at x = 0), we compute lim h→0 f(h) — f(0) h lim 0+4 (c) To determine whether f is differentiable at x = 1, we compute lim h→0+ lim h→0- ƒ(1+ h) − f(1) h f(1+h) − f(1) h - = lim 2h/3/h h→0+ = lim h→0- (d) Classify the differentiability of f at each of the points. f is differentiable at x=a 1. x = 1 f has a vertical tangent line at x=a 2. x = 0 f has a cusp at x=a 3. x=-1 = 2/3 = 2/3
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...
Related questions
Question
100%
Solutions to the red boxes please
Transcribed Image Text:Consider the function
x²+2x-1 if x-1
f(x)=√√8x
2x+4
3
if 1<<1
if x 1
(a) To determine whether of is differentiable at x = -1, we compute
lim
h→0+
2/3
ƒ(−1 + h) − f(−1)
h
=
lim
h→0+
lim
h→0-
0
f(-1+h) − f(-1)
h
=
lim
h→0-
(b) To determine whether f is differentiable at x =
lim
h→0
f(h) - f(0)
h
lim
h→0
(c) To determine whether f is differentiable at x =
lim
h→0+
f(1+ h) − f(1)
h
f(1+h) − f(1)
-
= lim 2h/3/h
h→0+
lim
h→0-
h
lim
h→0-
(), we compute
1, we compute
(d) Classify the differentiability of f at each of the points.
f is differentiable at x=a
1. x=1
f has a vertical tangent line at x=a 2. x = 0
f has a cusp at x=a
3. x = -1
=
2/3
= 2/3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Define the problem
VIEWStep 2: Determine the function f(x) is differentiable at x=-1 or not
VIEWStep 3: Continuation
VIEWStep 4: Determine the function f(x) is differentiable at x=0 or not
VIEWStep 5: Determine the function f(x) is differentiable at x=1 or not
VIEWStep 6: Continuation
VIEWSolution
VIEW
Step by step
Solved in 7 steps with 22 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning