Derivative Lab
From the idea of slope to optimization and related rates.
Derivative Lab starts with the idea behind every derivative: how fast something changes. Students read the average rate of change from a table, see a secant line become a tangent line and then learn the power rule, the derivatives of sine, cosine, e to the x and the natural log, and the product, quotient and chain rules.
The game then puts derivatives to work. Students write the equation of a tangent line, find critical numbers, use the first and second derivative tests with sign charts, and find concavity and inflection points. The last levels cover velocity and acceleration, optimization with fences, boxes and profit, and related rates with a ladder, circle, cube or sphere.
What children practice
- Find average rate of change from a table and see how it leads to a derivative
- Differentiate powers, sine, cosine, e to the x and the natural log
- Use the product, quotient and chain rules
- Write the equation of a tangent line at a point
- Find critical numbers, relative extremes, concavity and inflection points
- Solve velocity, optimization and related-rate problems with clean numbers
Levels
- Level 1: Rates of change
- Level 2: Power rule
- Level 3: sin, cos, e^x, ln x
- Level 4: Product and quotient
- Level 5: Chain rule
- Level 6: Critical points
- Level 7: Motion and rates
- Level 8: Course mix
How it works
- Eight levels run from rates of change to motion, optimization and related rates, with a mixed final level.
- Tangent lines are drawn through the real point with the real slope, and sign charts come from the real derivative.
- Each level opens after five right answers and the practice timer, so students build the rules in order.
- Answers keep the order of the terms in the function, and rates carry units in feet, seconds or inches as the prompt says.
Best for: A good fit for grades 11 to 12 in a first calculus course, when students know the rules but need practice choosing the right one.
Tip for parents: Ask your child to describe a speedometer reading and then the distance traveled. Saying which one is the derivative of the other makes the whole subject easier to hold.
Questions parents ask
Does the game teach limits?
Only as an idea, through tables of values in Level 1. Full work with limits, continuity and area is in Integral Lab.
Are the optimization problems realistic?
They are classic and clean, with fences, boxes and profit, and the numbers are chosen so the answers come out neatly.
How are derivative answers written?
Powers use real superscripts and other exponents use brackets after a caret, and a derivative keeps the order of the terms in the original function. This gives each answer one written form.
Ready to try it?
Derivative Lab is free with a parent account. A parent adds a child profile, and the child's progress is saved.