MonotonicityHard
Question
Which of the following statements is/are correct ?
Options
A.x + sinx is increasing function
B.sec x is neither increasing nor decreasing function
C.x + sinx is decreasing function
D.sec x is an increasing function
Solution
Let f(x) = x + sinx
⇒ f′(x) = 1 + cos x
As f′(x) ≥ 0∀ x ∈ R, f(x) is increasing
Let g(x) = sec x
g′ (x) = sec x tan x
g′ (x) changes sign.
g(x) is neither increasing nor decreasing.
⇒ f′(x) = 1 + cos x
As f′(x) ≥ 0∀ x ∈ R, f(x) is increasing
Let g(x) = sec x
g′ (x) = sec x tan x
g′ (x) changes sign.
g(x) is neither increasing nor decreasing.
Create a free account to view solution
View Solution FreeMore Monotonicity Questions
The function y = increases in the interval-...The number of strictly increasing functions f from the set $\{ 1,2,3,4,5,6\}$ to the set $(1,2,3,\ldots,9)$ such that $f...If f(x) = a{a| x | sgn x} ; g(x) = a[a| x | sng x] for a > 0, a ≠ 1 and x ∈ R, where {} & [ ] denote the ...If f(0) = f(1) = f(2) = 0 & function f(x) is twice differentiable in (0, 2) and continuous in [0, 2]. Then which of the ...f (x) = x2 + ax2 + bx2 + bx + 5 sin2 is an increasing function in the set of real numbers if a and b satisfy the conditi...