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
View Solution FreeMore Set, Relation and Function Questions
If the coefficient of x7 in equals the coefficient of x-7 in , then a and b satisfy the relation...In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y) | x, y ∈ A and x < y}. Then R is -...Number of integral elements contained in the range of function f(x) = sin-1 is -...If 0 ≤ [x] < 2 , - 1 ≤ [y] < 1 and 1 ≤ [z] < 3 where [·] denotes the greatest integer functio...Let a relation R in the set N of natural numbers be defined as (x, y) ∈ R if and only if x2 − 4xy + 3y2 = 0 ...