Calculus Tutorial

How to Find Critical Points on Windows with SumWise

For a smooth function, a critical point is an x-value where the derivative equals zero. These points can identify a local minimum, a local maximum, or another place where the graph becomes flat.

Explore Calculus in One Windows App

See how critical points fit alongside derivatives, integrals, tangent lines, and graphing in Offline Calculus Software for Windows.

Find the Critical Point

Enter this verified SumWise 2.3 expression:

critical_points(x^2 - 4*x + 4, x)

SumWise returns:

x = 2

What the Result Means

The polynomial x^2 - 4*x + 4 is the same as (x - 2)^2. Its slope is zero at x = 2, so that x-value is the critical point. Because the parabola opens upward, the point is also its local minimum, at (2, 0).

Inspect It on a Graph

Use the supported extrema graph workflow with an explicit range:

graph_extrema(x^2 - 4*x + 4) from -2 to 6

The graph provides a visual check: the curve falls toward x = 2, reaches its lowest point, and rises again. Zoom, pan, reset, and curve inspection controls can help you examine the neighborhood around the point.

Current SumWise 2.3 Scope

critical_points() supports scoped polynomial workflows; it is not a universal critical-point solver. For example, critical_points(sin(x)) is not supported by the current public analysis.

Runs Locally

Once SumWise is installed, this calculation and graph preparation run locally in the Windows application rather than through a web calculation service.

Try SumWise on Windows

Explore supported calculus and graphing workflows during the full-featured seven-day trial.

Try SumWise free for 7 days