Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

Rolle's theorem is applicable in the interval [-2, 2] for the function

1) f (x) = x2

2) f (x) = 4x4

3) f (x) = 2x3 + 3

4) f (x) = π|x|

Solution: (2) f (x) = 4x4

f (x) = 4x4, then

(i) f (x) is continuous in (−2, 2)

(ii) f (x) is differentiable in (−2, 2)

(iii) f (−2) = f (2)

f (x) = 4x4 satisfies all the conditions of Rolle’s theorem, therefore a point c such that f ′(c) = 0

⇒16c3 = 0

⇒ c = 0 ∈ (−2, 2)

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