Application of DerivativeHard
Question
If f(x) satisfies the requirements of Lagrange′s mean value theorem on [0, 2] and if f(0) = 0 and f′(x) ≤ 1/2 ∀ x ∈ [0, 2], then
Options
A.| f(x) | ≤ 2
B.f(x) ≤ 1
C.f(x) = 2x
D.f(x) = 3 for at least one x in [0, 2]
Solution
For x ∈ (0, 2)
f′(c) =
(Here c ∈ (0, x))
⇒ f(x) = 2.f′(x)
f(x) ≤1
f′(c) =
(Here c ∈ (0, x))⇒ f(x) = 2.f′(x)
f(x) ≤1
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