Given f(x) = cos − 1 
, where sgn ( ) denotes the signum function and [ . ] denotes the greatest integer function. Discuss the continuity and differentiability of f (x) at x = ± 1.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
f is continuous & derivable at x = − 1 but f is neither continuous nor derivable at x = 1
Sol. f(1) = 0
R.H.L. = 
f(1 + h) = 
cos –1 
= 
cos –1 
= 0
L.H.L. = 
f(1 – h) = 
cos –1 
= cos –1 (0) = 
f(–1) = 0
∴ f(x) is discontinuous hence non-derivable at x = 1
f ′ (–1 + ) = 
= 0 and f ′ (–1 – ) = 
= 0
⇒ f ′ (–1 + ) = f ′ (–1 – ) = 0
∴ f(x) is derivable at x = – 1
──────────────────────────────────────────────────────────────────────────────────────────
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