Let a be a conostant and let f(x)={x^(3)-ax, if x<1                                                      {x^(4), if x>=1 then (a) f is continuous at 0 only if a=0 (b) f is differentiable at 1 for all a (c) f'(1)=3-a for all a (d) f'(0) exists only if a=0 (e) none of these

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Let a be a conostant and let f(x)={x^(3)-ax, if x<1

                                                     {x^(4), if x>=1

then

(a) f is continuous at 0 only if a=0

(b) f is differentiable at 1 for all a

(c) f'(1)=3-a for all a

(d) f'(0) exists only if a=0

(e) none of these

Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Interpolation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,