Mark all true statements (there might be more than one statement that is true). O Let f: AC R→ R and assume that, for all x, ye A, f(x) = f(y). Then for all c E Int(A), f'(c) = 0. x²sin :) if x # 0 Let f: R→ R be given by f(x) = { 0 Let f: (a, b) → R be differentiable on (a,b) and assume that f' is continuous at c € (a, b). If f'(c) >0 then there is > 0, such that for all x, y = D(c,d) n (a,b), if x
Mark all true statements (there might be more than one statement that is true). O Let f: AC R→ R and assume that, for all x, ye A, f(x) = f(y). Then for all c E Int(A), f'(c) = 0. x²sin :) if x # 0 Let f: R→ R be given by f(x) = { 0 Let f: (a, b) → R be differentiable on (a,b) and assume that f' is continuous at c € (a, b). If f'(c) >0 then there is > 0, such that for all x, y = D(c,d) n (a,b), if x
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 48E
Related questions
Question
Please pick all the right options thanks
![Mark all true statements (there might be more than one statement that is true).
O Let f:ACR → R and assume that, for all x, y € A, f(x) =f(y). Then for all c = Int(A), f'(c) = 0.
Let f: R→ R be given by f(x) =
QUESTION 2
f(x)=f(x) +
x-sin
(-)
0
Let f: (a, b) → R be differentiable on (a,b) and assume that f' is continuous at c € (a,b). If f'(c) > 0 then there is 8 >0, such that for all x, y € D(c, 8) n (a,b), if x<y then f(x) <f(y).
○ Let f, g: AC R→ R be differentiable for all x € Int(A) and f'(x) = g'(x), for all x € Int(A). Then there is C € R, such that f(x) = g(x) + C.
O Let f: A c R → R be differentiable for all x € Int(A) and f'(x) = 0. Then f is constant.
f'(xo)
1!
Let f: (a, b).
Mark all true statements (there might be more than one statement that is true).
1
Let f: R→R be given by f(x) = |x|³. Then f is a class 6¹ function on R.
if x # 0
0
Suppose that f and its first n derivatives are continuous on [a,b], differentiable on (a,b) and x € [a,b]. Then for each x = [a, b], there is c in the interval with the endpoints x and x, such that
0
f(n) (xo)
f(n+1) (c)
(n+1)!
(x-x₂) +
n!
Suppose that f is differentiable on an interval (a, b). If f is not injective on (a,b), then there exists a point c = (a, b) such that f'(c) = 0.
x³sin
-(-)
X
if x=0
f''(xo)
2!
A function f: AC R→ R given by f(x) = -
-x₂)
. Then f' is continuous.
(X-X)
2
+
+
if x #0
if x=0
- (x − x) ¹+
is a class ² function on R.
(X-X₂)
n+1
→ R be differentiable on (a,b). Then f'(x) > 0 for all x € (a,b) if and only if f is strictly increasing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2F30d19f4d-bad3-44e4-8259-5b5b8e668167%2F2js60bs_processed.png&w=3840&q=75)
Transcribed Image Text:Mark all true statements (there might be more than one statement that is true).
O Let f:ACR → R and assume that, for all x, y € A, f(x) =f(y). Then for all c = Int(A), f'(c) = 0.
Let f: R→ R be given by f(x) =
QUESTION 2
f(x)=f(x) +
x-sin
(-)
0
Let f: (a, b) → R be differentiable on (a,b) and assume that f' is continuous at c € (a,b). If f'(c) > 0 then there is 8 >0, such that for all x, y € D(c, 8) n (a,b), if x<y then f(x) <f(y).
○ Let f, g: AC R→ R be differentiable for all x € Int(A) and f'(x) = g'(x), for all x € Int(A). Then there is C € R, such that f(x) = g(x) + C.
O Let f: A c R → R be differentiable for all x € Int(A) and f'(x) = 0. Then f is constant.
f'(xo)
1!
Let f: (a, b).
Mark all true statements (there might be more than one statement that is true).
1
Let f: R→R be given by f(x) = |x|³. Then f is a class 6¹ function on R.
if x # 0
0
Suppose that f and its first n derivatives are continuous on [a,b], differentiable on (a,b) and x € [a,b]. Then for each x = [a, b], there is c in the interval with the endpoints x and x, such that
0
f(n) (xo)
f(n+1) (c)
(n+1)!
(x-x₂) +
n!
Suppose that f is differentiable on an interval (a, b). If f is not injective on (a,b), then there exists a point c = (a, b) such that f'(c) = 0.
x³sin
-(-)
X
if x=0
f''(xo)
2!
A function f: AC R→ R given by f(x) = -
-x₂)
. Then f' is continuous.
(X-X)
2
+
+
if x #0
if x=0
- (x − x) ¹+
is a class ² function on R.
(X-X₂)
n+1
→ R be differentiable on (a,b). Then f'(x) > 0 for all x € (a,b) if and only if f is strictly increasing.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 6 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage