Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If f (x ) = 
Then -
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,c,d)
For x ∈ [–1, 2), f ′ (x) = 6x + 12 > 0 on (–1, 2), so f increases on [–1, 2]. f is trivially continuous on [–1, 3] except possibly x = 2. At point x = 2, f(2) = 35 and
f (x) = 
(37 – x) = 35,
f(x) = 
(3x 2 + 12x – 1)
= 3 × 4 + 12 × 2 – 1 = 35.
Thus, f is continuous at x = 2 as well. Now
f ′ (2+) = 
= 
= – 1
Similarly f ′ (2 –) = 24 ≠ f ′ (2+)
As f increases on [–1, 2] and decreases on [2, 3]
so f has a maximum value at x = 2.
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