## How do you find the local minimum and maximum?

When a function’s slope is zero at x, and the second derivative at x is:

1. less than 0, it is a local maximum.
2. greater than 0, it is a local minimum.
3. equal to 0, then the test fails (there may be other ways of finding out though)

What is local minimum?

The local minimum is a point within an interval at which the function has a minimum value. The relative minima is the minimum point in the domain of the function, with reference to the points in the immediate neighborhood of the given point.

What are local maximum values?

A local maximum point on a function is a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points “close to” (x,y).

### How do you find the maximum and minimum of a function?

Use basic rules of algebra to rearrange the function and solve the value for x, when the derivative equals zero. This solution will tell you the x-coordinate of the vertex of the function, which is where the maximum or minimum will occur. into the original function and solve to find the minimum or maximum.

How do you find the local maximum value?

To find the local maximum, we must find where the derivative of the function is equal to 0. Given that the derivative of the function yields using the power rule . We see the derivative is never zero. However, we are given a closed interval, and so we must proceed to check the endpoints.

What is a local minimum on a graph?

The graph of a function y = f(x) has a local maximum at the point where the graph changes from increasing to decreasing. At this point the tangent has zero slope. The graph has a local minimum at the point where the graph changes from decreasing to increasing.

#### What is the local minimum of a graph?

The graph of a function y = f(x) has a local maximum at the point where the graph changes from increasing to decreasing. At this point the tangent has zero slope. The graph has a local minimum at the point where the graph changes from decreasing to increasing. Again, at this point the tangent has zero slope.