Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Consider the function for x ∈ [–2, 3]
f(x) = 
. The value of c obtained by applying Rolle's theorem for which f ′
Text Solution
Verified by ExpertsThe correct answer is:
C
= x 2 – x – 6
⇒ f(x) = 
f(x) = – 6 ; 
f(x) = – 6
⇒ LHL = RHL = f(1) ∴ f(x) is continuous
LHD at x = 1 is 1
RHD at x = 1 is 1
∴ f(x) is differentiable at x = 1
f( – 2) = 0 ; f(3) = 0
all the conditions of Rolle ’ s are holding
f'(x) = 2x – 1 = 0
⇒ x = 
∴ 
∈ [ – 2, 3]
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