Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) = x < 2 x² +3 x ≥2 (3x²-5

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...
icon
Related questions
Question
100%
Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit
does not exist, type DNE.
f(x)
-
(3x²_5_x 2
x²+3 x ≥ 2
ƒ(2) =
lim f(x) =
x→2
ƒ(2)
Is f(x) continuous at x = 2? (Yes
x-2-
ƒ'(x) =
lim_ƒ'(x) =
lim
x→2
lim_ƒ'(x) =
x→2+
II
Is f(x) differentiable at x = 2? (No due to a cusp
x < 2
x > 2
Transcribed Image Text:Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined or a limit does not exist, type DNE. f(x) - (3x²_5_x 2 x²+3 x ≥ 2 ƒ(2) = lim f(x) = x→2 ƒ(2) Is f(x) continuous at x = 2? (Yes x-2- ƒ'(x) = lim_ƒ'(x) = lim x→2 lim_ƒ'(x) = x→2+ II Is f(x) differentiable at x = 2? (No due to a cusp x < 2 x > 2
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning