Maxima and MinimaMedium
Question
If ax + b/x ≥ c for all positive x, where a, b > 0, then-
Options
A.ab < 
B.ab ≥
C.ab ≥ 
D.None of these
Solution
Let f(x) = ax + 
- c ; x > 0 ; a, b > 0
⇒ f′(x) = a -
f’(x) = 0 ⇒ a -
= 0
⇒ x =
but ax +
≥ c; ∴ f(x) ≥ 0 for all x > 0.
⇒
≥ 0
⇒ a
+ b 
- c ≥ 0
⇒ 2
≥ c
⇒ ab ≥
- c ; x > 0 ; a, b > 0⇒ f′(x) = a -
f’(x) = 0 ⇒ a -
= 0⇒ x =
but ax +
≥ c; ∴ f(x) ≥ 0 for all x > 0.⇒
≥ 0⇒ a
+ b - c ≥ 0⇒ 2
≥ c⇒ ab ≥
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