Set, Relation and FunctionHard
Question
The function f : R → R given by f(x) = x(tan-1x)2 is -
Options
A.continuous and differentiable on R.
B.continuous but not differentiable on R.
C.monotonically increasing on R.
D.such that f′(x) is continuous and differentiable on R.
Solution
f′(x) = tan-1x
≥ 0 ∀ x ∈ R
∴ both f & f′ are continuous & differentiable on R.
≥ 0 ∀ x ∈ R∴ both f & f′ are continuous & differentiable on R.
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let f: → be a function given by f(x) = max(sinx, tan2x). Identify the correct statement(s) -...A set is defined as A = {x : x is irrational and 0.1 < x < 0. 101} then :...The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on the set A = {1, 2, 3} is -...Let f(x) = , then number of real points in the domain of f(x) for which f′(x) does not defined...If A = {x | x/2 ∈ Z, 0 ≤ x ≤ 10}, B = {x | x is one digit prime} C = {x | x/3 ∈ N, x ≤ 12}...