It is important to note that the Second Derivative Test can only be applied to a function that is twice differentiable, and that it only gives information about the extrema at a single point, not on an interval.Ĭonsider the function f(x) = x^2. If the second derivative is zero at a critical point, the test is inconclusive and further analysis is needed. If the second derivative is negative at a critical point, the function has a local maximum at that point.Ħ. If the second derivative is positive at a critical point, the function has a local minimum at that point.ĥ. Evaluate the second derivative at each critical point.Ĥ. Find the second derivative of the function.ģ. Find the critical points of the function by setting the first derivative equal to zero and solving for x.Ģ. Here are the steps to use the Second Derivative Test:ġ.
It is based on the fact that the sign of the second derivative of a function can indicate whether a critical point is a maximum, minimum, or neither.
The Second Derivative Test is a powerful tool in calculus that can be used to determine the nature of extrema (maxima and minima) of a function.
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