EMC Q.38
- Option : B
- Explanation :
Given function is, f(x) = 3x4 - 4x2 + 5
(i) f (x) is continuous in every real interval
(ii) f ' (x) exist in any real interval
(iii) f(-1) = 3(-1)4 - 4(1)2 + 5 = 4
f(1) = 3(1)4 - 4(1)2 + 5 = 4
f(-1) = f(1)
Also f ' (c) = 12c3 - 8c = 0
⇒ c = 0,
c ∈ [-1, 1]Hence all the condition of Rolle's Theorem are satisfied in the interval [-1, 1]
