Find the extrema using the second derivative test
👉 Learn how to find the extrema of a function using the second derivative test. The second derivative test states that if a function has a critical point for which f'(x) = 0, and the second derivative is positive, then the function has a minimum point at that point. If the second derivative is negative, then the function has a maximum point at that point and if the second derivative is zero, then the function has an inflection point at that point.
To find the extrema of a function using the second derivative test, we first find the derivative of the function and equate it to zero. Then, we solve the resulting equation for x to get the critical points. Then take the second derivative of the function and substitute each of the critical points into the second derivative. The critical points for which the second derivative is positive represent minimum points, the critical points for which the second derivative is negative represent maximum points, while the critical points for which the second derivative is zero represent inflection points.
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