Question
If $a x+\frac{b}{x} \geq c$ for all positive $x$, where $a, b>0$, then(A) $a b<\frac{c^{2}}{4}$(B) $a b \geq \frac{c^{2}}{4}$(C) $a b \geq \frac{c}{4}$(D) None of these
Step 1
We can rewrite this inequality as $f(x) = a x+\frac{b}{x} - c \geq 0$. Show more…
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If $a x+\frac{b}{x} \geq c$ for all positive $x$, where $a, b>0$, then (A) $a b<\frac{c^{2}}{4}$ (B) $a b \geq \frac{c^{2}}{4}$ (C) $a b \geq \frac{c}{4}$ (D) None of these
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Inequalities
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