State whether f(x) = tanx – x is increasing or decreasing its domain.
f(x) = tan x – x
f’(x) = Sec2x – 1
Sec2x – 1 ≥ 0
Sec2x ≥ 1
1 + tan2x = Sec2x
1 + tan2x ≥ 1
tan2x ≥ 0
tan2x ≥ 0 ∀x ϵ [0, 2π]
f(x) is increasing its domain.
1
State whether f(x) = tanx – x is increasing or decreasing its domain.
f(x) = tan x – x
f’(x) = Sec2x – 1
Sec2x – 1 ≥ 0
Sec2x ≥ 1
1 + tan2x = Sec2x
1 + tan2x ≥ 1
tan2x ≥ 0
tan2x ≥ 0 ∀x ϵ [0, 2π]
f(x) is increasing its domain.