## 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:

- less than 0, it is a local maximum.
- greater than 0, it is a local minimum.
- 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.