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Now, the second derivative of the function tells us the rate of change of the first derivative. It therefore follows that if the second derivative is positive at the stationary point, then the gradient is increasing. The fact that it is a stationary point in the first place means that this can only be a minimum. Conversely, if the second derivative is negative at that point, then it is a maximum. Now, if the second derivative is zero, we have a problem. It could be a point of inflexion, or it could still be an extremum. Examples of each of these cases are below-all have a second derivative equal to zero at the stationary point in question: 1  has a point of inflexion at.
partial derivative. noun, Mathematics. 1. the derivative of a function with respect to one of its variables with all other variables held constant. partial derivative. 1. the derivative of a function of two or more variables with respect to one of the variables, the other or others being considered constant. partial derivative.