Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f(x) = 
The values of the coefficients a and b for which the function is continuous and has a derivative at x 0 , are
Text Solution
Verified by ExpertsThe correct answer is:
B
For f to be continuous everywhere, we must have 
= f(x 0 )
= 
f(x) = ax 0 + b
Also, f has a derivative at x 0 if f ′ (x 0 + ) = f ′ (x 0 – )
Now, f ′ (x 0 +) = 
= 
= 
= 
a = a
[ 
= ax 0 + b]
and f ′ (x 0 –) = 
= 
= 
= 
(h + 2x 0 ) = 2x 0
That is, a = 2x 0 , and hence b = 
– ax 0 = 
–2 
= – 
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