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CurveLab: A Function Analyzer on Steroids for Years 9-12
- Digital Technologies Institute PTY LTD
- Jul 14
- 5 min read
Now live on MyComputerBrain, CurveLab brings powerful mathematical function analysis into a single, accessible learning environment.
It is free on MyComputerBrain, does not require student accounts, and does not make use of GenAI, which makes it easy to use in class, for homework, or for independent revision.
Built for mathematical reasoning and repeated classroom and home use, CurveLab combines graphing, symbolic differentiation, numerical feature detection, and written analysis in one place. Students explore their functions, interpret derivatives and check their own work in an integrated environment.
Students enter a function and receive a structured explanation of the graph and its key features, including x-intercepts, y-intercepts, minima, maxima, turning points, concavity, and points of inflection.
Why CurveLab matters
The main value of CurveLab is speed of feedback.
When students can quickly see whether a graph, derivative, intercept, turning point, or classification is correct, they can confirm or correct their thinking while the reasoning is still active. That shortens the gap between attempt and response.
CurveLab makes that possible by bringing the graph, the marked points, and the written analysis together in one place. Students can test an idea, inspect the result, and adjust their mental model immediately.
Useful from Year 9 onward
CurveLab is especially relevant in senior secondary mathematics, but it is also useful earlier.
From Year 9 onward, students begin to encounter functions and identify basic graph features such as:
x-intercepts
y-intercepts
the overall shape of a graph
the connection between an equation and its visual representation
At this stage, CurveLab helps students build familiarity with function notation and graph behaviour.
It is also useful for solving quadratic expressions, because the solutions of f(x)=0 appear directly as the graph’s x-intercepts. That gives students a concrete bridge between algebraic solving and visual reasoning.
What students actually do
CurveLab is intentionally simple to use.
Students enter a function, choose an interval manually or use Auto view, and then inspect the analysis produced by the tool. The graph and the written explanation work together:
the graph shows f(x), f'(x), and f''(x)
key points are marked directly on the curve
the written explanation is organised by mathematical concept
students can zoom, pan, hide or show graphs, and focus on one relationship at a time
This makes CurveLab suitable for several kinds of work:
introducing functions and graph behaviour
practising curve sketching
revising differential calculus
checking hand-calculated derivatives
discussing misconceptions in whole-class teaching
Main features
Combined graph and analysis view
Students see a plotted curve together with a structured written explanation of important features such as intercepts, minima, maxima, turning points, concavity, and points of inflection.
Automatic derivative generation
CurveLab computes derivatives and uses them to analyse stationary points, turning points, concavity, local extrema, and points of inflection.
Marked points on the graph
Important points are shown directly on the graph so students can move between the visual representation and the written reasoning.
Linked graph and analysis text interaction
The graph and the written analysis are connected. Hovering over a marked point in the graph highlights the corresponding point in the analysis, and hovering over the point in the analysis shows it on the graph.
Graph comparison
f(x), f'(x), and f''(x) can be shown or hidden to help students compare how the derivative graphs relate to the original function.
Adjustable interval selection
Students can enter their own interval or use Auto view to focus on the most relevant part of the graph.
A derivative checker
Students can enter their own version of f'(x), f''(x), or f'''(x) and compare it against CurveLab’s result numerically across the selected interval.
Support for common senior-school notation
CurveLab handles powers, rational expressions, trigonometric functions, exponential and logarithmic functions, square roots, absolute value, inverse tangent, and related notation used in school mathematics.
Why the derivative checker matters
One of the strongest features of CurveLab is the derivative checker.
Students often assume that if their derivative does not look exactly the same as the model answer, it must be wrong. In practice, equivalent expressions can be written in different forms.
CurveLab compares student-entered derivatives numerically over the selected interval. That means a student’s answer can still be accepted if it gives the same values, even when the expression looks different on the page.
This matters for teaching because it keeps the focus on mathematical equivalence.
It also supports a faster feedback loop. Students do not have to stay uncertain for long about whether a result is correct. They can test it while the reasoning is still active, which makes correction and consolidation more immediate.
Designed for teaching
CurveLab is useful because it is structured for learning.
The analysis is grouped by concept in a clear, structured way.
The interval can be controlled, which matters for classroom questions.
The tool intentionally does not fully simplify every derivative, so students can still see the underlying differentiation structure.
The graph and the text analysis are designed to support each other.
This makes the tool useful for teacher explanation, guided practice, paired discussion, and independent checking.
Classroom use
CurveLab works well in lessons where students first predict a graph’s features and then test those predictions.
A typical lesson flow might look like this:
Students are given a function and asked to sketch its likely behaviour.
They calculate derivatives by hand.
The class enters the function into CurveLab.
Students compare the generated analysis with their own predictions.
They revise their sketch and explain what they would now change.
This approach keeps the tool in a supporting role. CurveLab is most valuable when it helps students refine mathematical reasoning, not when it replaces it.
Use at home
CurveLab is also well suited to revision outside class.
Students can use it to:
test textbook functions
revisit difficult curve-sketching questions
compare their own derivative work
zoom into difficult regions of a graph
rewrite the generated explanation in their own words
This makes it a practical bridge between direct instruction and independent study.
A new mathematics tool for MyComputerBrain
CurveLab continues the mission of MyComputerBrain to open up black boxes.
CurveLab fills that role for functions and introductory calculus.
For teachers, it offers a practical way to connect algebra, graphs, derivatives, and feedback in one interface. For students, it offers a clearer path from symbolic procedure to mathematical understanding.
CurveLab does not make use of generative AI. Its graphing, differentiation, and analysis are fully deterministic, so the same input produces the same result every time.
