Mathematical Physics - Maxima and Minima : First Derivative Test / Sign Scheme for f’(x)
When a function f(x) is either maximum or minimum or stationary then f’(x)=0. But how we can decide that the function is either maximum or minimum or stationary? The first derivative test is the mathematical tool for the answer of this question. If f(x) is extremum at x=a then when f’(x)changes its sign from positive to negative at x=a then f(x) has a local maximum value at this point. In reverse condition the function has a local minimum value at x=a. If there is no change of sign of f’(x) then the function is neither maximum nor minimum at x =a.
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