Set, Relation and FunctionHard
Question
Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = ex2 + e- x2, g(x)= xex2 + e- x2 and h (x) = x2 ex2 + e- x2 . If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then
Options
A.a = b and c≠ b
B.a = c and a ≠ b
C.a ≠ b and c ≠ b
D.a = b = c
Solution
f(x) = ex2 + e- x2 ⇒ f′(x) = 2x(ex2 + e- x2) ≥ 0 ∀ x ∈ [0, 1]
Clearly for 0 ≤ x ≤ 1 f(x)≥ g(x) ≥ h(x)
∵ f(1) = g(1) = h(1) = e +
and f(1) is the greatest
∴ a = b = c = e + ⇒ a = b = c.
Clearly for 0 ≤ x ≤ 1 f(x)≥ g(x) ≥ h(x)
∵ f(1) = g(1) = h(1) = e +
and f(1) is the greatest∴ a = b = c = e +
⇒ a = b = c.Create a free account to view solution
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