Maximum Value of a Product Using Logarithmic Differentiation

Maximum Value of a Product Using Logarithmic Differentiation

For a positive function:

$$P(x)=u(x)v(x)$$

the stationary condition can be obtained from:

$$\frac{P'(x)}{P(x)}=\frac{u'(x)}{u(x)}+\frac{v'(x)}{v(x)}$$

Usage

- Useful for maximizing products where direct differentiation is cumbersome.

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