How do you know when you've reached the local maximum?

1. How do you know if its a local maximum or minimum?
2. How do you find the local maximum?
3. How do you know if a maximum is local or global?
4. What happens at a local maximum?

How do you know if its a local maximum or minimum?

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.

How do you find the local maximum?

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.

How do you know if a maximum is local or global?

At all the minima points, the first order derivative will be zero and related value can be found where the local or global minima occurred. Similarly, the point where function takes the maximum value is called as global maxima. Other points will be called as local maxima.

What happens at a local maximum?

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).