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.
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