Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Check differentiability of f(x) = sgn (x 2/3 ) + 
+ |x – 1| 5/3 in [–2, 2] where [.] denotes GIF.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Differentiable in [–2, 2]
Sol. |x – 1| 5/3 is differentiable for all x
Let g(x) = sgn(x 2/3 ) + 
⇒ g'(0) = 
= 
= 0
so differentiable at 0.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Test the continuity & differentiability of the function defined as under at x = 1 & x = 2.
f (x) =
A function f is defined as follows: f(x) =
Discuss the continuity & differentiability at x = 0 & x…
Prove that f (x) = |x| cos x is not differentiable at x = 0
Show that the function f (x) = is,
(i)differentiable at x = 0, if m > 1.
(ii)continuous but not di…
Examine the differentiability of f (x) = at x = 0.
If f(x) = is derivable at x = 1. Find the values of a & b.