How to find relative maximum and minimum

Remark: I deliberately avoided the second derivative test alluded to in the OP.


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This is because in my experience, first year calculus students who use the second derivative test tend to get into difficulties more than students who look at the behaviour of the first derivative. Home Questions Tags Users Unanswered.

Finding a Function based on Relative min and max Ask Question. Asked 4 years, 9 months ago. Active 4 years, 9 months ago.

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Maxima and Minima of Functions of Two Variables

Email Required, but never shown. Featured on Meta. In other words, the extrema of a function are contained among its critical points.

Maximum and Minimum Values of Polynomials

Note that the necessary condition does not guarantee the existence of an extremum. Local extrema of differentiable functions exist when the sufficient conditions are satisfied. These conditions are based on the use of the first-, second-, or higher-order derivative. Now we turn to their formulation and proof.

We confine ourselves to the case of the minimum.

Example Questions

The second derivative test is convenient to use when calculation of the first derivatives in the neighborhood of a stationary point is difficult. Then if.

Worked example: finding relative extrema - AP Calculus AB - Khan Academy

The derivative is given by. The maximum value that is the value of the function at the maximum point is equal to.

Solved Problems

The function is differentiable on the whole set of real numbers. Therefore, the extremum points are contained among the stationary points where the derivative is equal to zero. By the first derivative test, this point is a local maximum point. This function belongs to the family of power-exponential functions. The minimum and maximum values, respectively, are equal to:. Example 1.