Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Given 
Iff (x) is differentiable at x = 1, then the value of |a – b|is
Text Solution
Verified by ExpertsThe correct answer is:
3
3
f(1 - ) = 1 = f(1) and f(1 + ) = a + b
For continuity at x = 1, a + b = 1 ......(i)
In 0 < x < 1, f’(x) = 2xe 2(x- x) + 2x 2 e 2(x- x)
In 1< x < 2, f’(x) = - 2a sin (2x - 2) + 2bx
f'(l + ) = 2b
For differentiability at x = 1, 2b = 4 . This with (i) gives the values a = - 1, b = 2
then |b - a| = 3
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
The value off (0) so that the function is continuous everywhere is k, then value of 10 k is
Let f, g and h are differentiable functions. If f (0) = 1; g (0) = 2; h (0) = 3 and the derivatives…
If is continuous in [ , 3 ], then the number of points at which f(x) is not differentiable is/are
If f is differentiable at x = 3, then the value of is equal to
If
and f (x) is continuous at x = 0, then the value of be is equal to
If is continuous at x=4
then value of is equal to