If `ax+b/x >= c` for all positive x, where ` a, b, c > 0,` then-

Options

A. `27ab^(2)ge4c^(3)`
B. `27ab^(2)le4c^(3)`
C. `9ab^(2)ge4c^(2)`
D. `9ab^(2)le4c^(2)`

Explanation

To solve the inequality \( ax + \frac{b}{x} \geq c \) for all positive \( x \), where \( a, b, c > 0 \), we will follow these steps:

### Step 1: Multiply the entire inequality by \( x \)
Since \( x \) is positive, multiplying by \( x \) does not change the direction of the inequality:
\[ ax^2 + b \geq cx \]

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