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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.
differentiable. If so, what do we call the derivative of a derivative? We call them higher order derivative. Consider the example of a position function for a falling object such as st t()=4.9 2. The derivative of s is the velocity function vt t( )=9.8 . The derivative of v is the acceleration function at()=9.8 (falling objects accelerate at a constant rate). The acceleration function is the second derivative of the position function. We denote the second derivative of s as s such that at v t s t() ()=='. Before finding higher order derivatives, we must turn to the issue of notation. If we let yfx= (), the derivative of f ()x can be written as f '()x or df dx or f i or Df xx ( ) or ...