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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CAT Formulas
Applications of Derivatives
Monotonicity of a Ratio
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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