High School Optimization (Max/Min) Calculator
Find local maxima and minima of a function using calculus derivatives.
Try: x^3 – 3x, sin(x), x^4 – 2x^2
Derivative f'(x)
Critical Points Found
Waiting for calculation…
Optimization Graph
About the Optimization (Max/Min) Calculator
Optimization is one of the most useful applications of calculus. It involves finding the absolute maximum or minimum values of a function, which corresponds to the “best” outcome in real-world scenarios—such as maximizing profit, minimizing cost, or optimizing surface area for a given volume.
Critical Points & Derivatives
The peaks (maxima) and valleys (minima) of a smooth graph occur where the tangent line is horizontal. This means the slope of the curve is zero.
To find these points algebraically:
- Find the derivative f'(x).
- Set f'(x) = 0 and solve for x. These x-values are called Critical Points.
- Use the First Derivative Test (checking sign changes) or Second Derivative Test to classify them as max or min.
Global vs. Local Extrema
A local maximum is the highest point in its immediate neighborhood. A global maximum is the highest point on the entire domain of the function. This Optimization (Max/Min) Calculator focuses on identifying local extrema within the viewing window you specify.
FAQ
Yes, this tool is completely free and runs in your browser using JavaScript.
The calculator scans numerically within the “View Interval” you set. If a maximum is outside this range (e.g., at x=100), it won’t be detected. Expand your interval to see more.
It specifically looks for maxima and minima (slope = 0). Points of inflection (where concavity changes) are not currently highlighted unless the slope is also zero there.
It uses a numerical scan with high precision, but extremely steep functions or tiny oscillations might result in approximations.