Consider two functions y = f(x) and y = g(x) defined as
f(x) = 
and
g(x) = 
(i) f(x) is continuous at x = 1 but not differentiable at x = 1, if
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Ans.
(i)
Sol. 
For continuity a + b = 4b i.e., a = 3b .....(i)
f(1 + ) = 
= 
= 
= 2b
f(1 – ) = 
= 
= 
= 2a
2a ≠ 2b, a ≠ b.
(ii)
Sol. 
= 
= 4c + d
= 
= 2d + 3 – c
g(2) = 4c + d
∴ 4c + d = 2d + 3 – c
∴ d = 5c – 3.
(iii)
Sol. 
, 
= 5a – 6
Since f(x) is continuous at x = 3
∴ 8b = 5a – 6 .....(i)
f ' (3 – ) = 
= 
= 2b
f '(3 + ) = 
= 
Since f is differentiable at x = 3
∴ 5a – 8b – 6 = 0
∴ f '(3 + ) = a – 1
Thus, a – 1 = 2b .....(ii)
From Esq. (i) and (ii), we get
a = 2, b = 
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