Show that the function f (x) = 
is,
(i)differentiable at x = 0, if m > 1.
(ii)continuous but not differentiable at x = 0, if 0 < m ≤ 1.
(iii)neither continuous nor differentiable, if m ≤ 0.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
f (x) = 
for continitity f(0) = 0 = RHL (x = 0)
[a finite quantity between [–1, 1]] = 0
It hold only when m > 0
if m ≤ 0 neither continuous nor derivable
for derivability 
= finite
it is finite and unique
and equal to zero if m > 1 when m >1 continuous and derivable
if 0 < m ≤ 1 continuous but not derivable
──────────────────────────────────────────────────────────────────────────────────────────
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