MonotonicityHard
Question
Consider the function for x = [-2, 3], f(x) = 
if x ≠ 1, then
if x ≠ 1, thenOptions
A.f is discontinuous at x = 1 ⇒ Rolle′s theorem is not applicable in [-2, 3]
B.f(-2) ≠ f(3) ⇒ Rolle′s theorem is not applicable in [-2, 3]
C.f is not derivable in (-2, 3) ⇒ Rolle′s theorem is not applicable
D.Rolle′s theorem is applicable as f satisfies all the conditions and c of Rolle′s theorem is 1/2
Solution
f(-2) = f(3) = 0
f(x) is continuous in [-2, 3] & derivable in (-2,3) so Rolle′s theorem is applicable. so ∃ c ∈ (-2, 3) such that f′(c) = 0
⇒
= 0 ⇒ c = 1/2
f(x) is continuous in [-2, 3] & derivable in (-2,3) so Rolle′s theorem is applicable. so ∃ c ∈ (-2, 3) such that f′(c) = 0
⇒
= 0 ⇒ c = 1/2Create a free account to view solution
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