Maxima and MinimaHard
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 ≥
Create a free account to view solution
View Solution FreeMore Maxima and Minima Questions
A rectangle has one side on the positive y-axis and one side on the positive x-axis. The upper right hand vertex on the ...The local maximum value of x(1 − x)2 ,0 ≤ x ≤ 2 is -...Let ƒ(x) = (x − p)2 + (x − q)2 + (x − r)2. Then ƒ(x) has a minimum at x = λ where λ...The minimum value of the function y = 2x3 - 21x2 + 36x - 20 is-...For x ∈ , define f(x). Then f has...