Application of DerivativeHard
Question
If f(x) = ln (x - 2) - 1/x, then
Options
A.f(x) is M.I. for x ∈ (2, ∞)
B.f(x) is M.I. for x ∈ [- 1, 2]
C.f(x) is always concave downwards
D.f-1(x) is M.I. wherever defined
Solution
f(x) = ln(x - 2) - 1/x
f′(x) =
=
As ln(x - 2) is defined when x > 2
⇒ f(x) is M.I. for x ∈ (2, ∞)
⇒ f-1(x) is M.I. wherever defined
Also f″(x) =
< 0
⇒ f(x) is always concave downward
f′(x) =
=
As ln(x - 2) is defined when x > 2
⇒ f(x) is M.I. for x ∈ (2, ∞)
⇒ f-1(x) is M.I. wherever defined
Also f″(x) =
< 0⇒ f(x) is always concave downward
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