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Minimum of a Function from Its Derivative Sign
If:
$$f'(x)<0\quad\text{for }x<c$$
and:
$$f'(x)>0\quad\text{for }x>c$$
then:
$$f(c)=\min f(x)$$
locally.
Usage
- Used to identify a minimum directly from the sign pattern of the derivative.
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Minimum of a Function from Its Derivative Sign
If:
$$f'(x)<0\quad\text{for }x<c$$
and:
$$f'(x)>0\quad\text{for }x>c$$
then:
$$f(c)=\min f(x)$$
locally.
Usage
- Used to identify a minimum directly from the sign pattern of the derivative.
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