# Local max and min with derivatives

##### 2020-02-24 18:36

how would first and second derivative help find the inflection point and local maxmin? 1 Difference between Gradient, Rate of Change and Derivative (Single Variable Calculus)The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f(x) 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f(x) 0 and the second derivative is negative at this point, then f has local maximum here. local max and min with derivatives

In the last video we saw that if a function takes on a minimum or maximum value, min max value for our function at x equals a, then a is a critical point. But then we saw that the other way around isn't necessarily true. x equal a being a critical point does not necessarily mean that the function takes on a minimum or maximum value at that point.

The First Derivative: Maxima and Minima Consider the function f(x) 3x44x312x23 on the interval [2, 3. We cannot find regions of which f is Finding Maxima and Minima using Derivatives. Where is a function at a high or low point? Calculus can help! A maximum is a high point and a minimum is a low point: In a smoothly changing function a maximum or minimum is always where the function flattens out (except for a saddle point). Where does it flatten out? Where the slope is zero.local max and min with derivatives This calculator evaluates derivatives using analytical differentiation. It will also find local minimum and maximum, of the given function. The calculator will try to simplify result as much as possible. There are examples of valid and invalid expressions at the bottom of the page.

## Local max and min with derivatives free

Because the second derivative equals zero at x 0, the Second Derivative Test fails it tells you nothing about the concavity at x 0 or whether theres a local min or max there. When this happens, you have to use the First Derivative Test. In this example, you find that there is neither a min nor a max at x 0; theres an inflection local max and min with derivatives Thus, the local max is located at (2, 64), and the local min is at (2, 64). Youre done. To use the First Derivative Test to test for a local extremum at a particular critical number, the function must be continuous at that xvalue.

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