![]() The maximum and minimum value can be understood through the below points. Here we consider a function f(x) defined on a closed interval I, and a point x= k belongs to a closed interval (I). The second derivative test is a systematic method of finding the maximum and minimum value of a closed value function defined on a closed or bounded interval. How Do You Find the Maximum and Minimum of Second Derivative Test? ![]() Also for a value x = k, if the second derivative value f'(k) = 0, then too the function fails. If for a given function f(x), the second derivative does not exist f''(x) = 0, then the test fails. The second derivative test fails in two instances. Why Does the Second Derivative Test Fail? If the second derivative test is not true, we go back to the first derivative test and verify for the given values. For situations of point of inflection, it does not hold true. The second derivative test is not always true. Is the Second Derivative Test Always True? Here the limiting points obtained from the first derivative are checked through the second derivative to find the maximum and the minimum point. ![]() ![]() The second derivative takes the first derivative and the second derivative of the given function. The first derivative test takes only the first derivative of the function, and takes a few points in the neighborhood of the given point, to find if it is the maximum or the minimum point. The first derivative test and the second derivative test are both helpful to find the local minimum and local maximum points. What Is the Difference Between First Derivative Test and Second Derivative Test?
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