Home » Cloud Investing Network » Where Is the Local Maximum?

Where Is the Local Maximum?

Maya Lin-Takahashi • • 6 min read
Where Is the Local Maximum?

A local maximum point on a function is a point (x,y) on the graph of the function

graph of the function
An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p(x, y) = 0. This equation is often called the implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x.
› wiki › Algebraic_curve
whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).

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 tell if a point is a local maximum?

For each value, test an x-value slightly smaller and slightly larger than that x-value. If both are smaller than f(x), then it is a maximum. If both are larger than f(x), then it is a minimum. If one is smaller and the other is larger than f(x), then it is an inflection point.

Maya Lin-Takahashi
Author

Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.