Monotonicity of a Ratio

Rarely Tested

Monotonicity of a Ratio

For positive differentiable functions $$f(x)$$ and $$g(x)$$:

$$\frac{d}{dx}\left(\frac{f}{g}\right)=\frac{gf'-fg'}{g^2}$$

Usage

- Used to determine whether a ratio is increasing or decreasing.

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