100 guided animations · 10 topic units · Free to explore
Make a prediction, change a value, and explain the result. Work through each unit in order or choose the topic you want to understand today. Every investigation has controls, a worked explanation, and a question to test your reasoning.
Your collection at a glance
Cubic derivatives
Investigations 1–10
The product rule
Investigations 11–20
Implicit circle tangents
Investigations 21–30
Signed accumulation
Investigations 31–40
Substitution and bounds
Investigations 41–50
Average function values
Investigations 51–60
Washer volumes
Investigations 61–70
Differential growth models
Investigations 71–80
Binomial probability
Investigations 81–90
Vector components and angles
Investigations 91–100
Related investigations use the same mathematical model with different questions and starting values. Reset restores the values used in that investigation’s worked answer. Read its assumptions before applying a model to a new situation.
100 animations · Showing 1–20
Grade 12 · Cubic derivatives
Cubic derivatives · Investigation 1 of 100
Cubic derivatives: investigate a stationary inflection at zero with cubic coefficient a = 1; linear coefficient b = 0.
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Cubic derivatives · Investigation 2 of 100
Cubic derivatives: investigate a cubic with two stationary points with cubic coefficient a = 1; linear coefficient b = -3.
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Cubic derivatives · Investigation 3 of 100
Cubic derivatives: investigate a strictly increasing cubic with cubic coefficient a = 1; linear coefficient b = 2.
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Cubic derivatives · Investigation 4 of 100
Cubic derivatives: investigate reverse the cubic direction with cubic coefficient a = -1; linear coefficient b = 0.
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Cubic derivatives · Investigation 5 of 100
Cubic derivatives: investigate a falling cubic with turning points with cubic coefficient a = -1; linear coefficient b = 3.
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Cubic derivatives · Investigation 6 of 100
Cubic derivatives: investigate a linear special case with cubic coefficient a = 0; linear coefficient b = 2.
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Cubic derivatives · Investigation 7 of 100
Cubic derivatives: investigate a flat zero function with cubic coefficient a = 0; linear coefficient b = 0.
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Cubic derivatives · Investigation 8 of 100
Cubic derivatives: investigate strong cubic and weak linear growth with cubic coefficient a = 2; linear coefficient b = 0.5.
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Cubic derivatives · Investigation 9 of 100
Cubic derivatives: investigate a shallow cubic with negative drift with cubic coefficient a = 0.5; linear coefficient b = -1.
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Cubic derivatives · Investigation 10 of 100
Cubic derivatives: investigate negative cubic with negative drift with cubic coefficient a = -0.5; linear coefficient b = -2.
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The product rule · Investigation 11 of 100
The product rule: investigate a growing exponential times x with linear shift a = 0; exponential rate b = 1.
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The product rule · Investigation 12 of 100
The product rule: investigate a decaying exponential times x with linear shift a = 0; exponential rate b = -1.
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The product rule · Investigation 13 of 100
The product rule: investigate a positive shifted factor with linear shift a = 2; exponential rate b = 0.5.
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The product rule · Investigation 14 of 100
The product rule: investigate a negative shifted factor with linear shift a = -2; exponential rate b = 0.5.
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The product rule · Investigation 15 of 100
The product rule: investigate a constant exponential factor with linear shift a = 1; exponential rate b = 0.
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The product rule · Investigation 16 of 100
The product rule: investigate cancellation at the origin with linear shift a = 1; exponential rate b = -1.
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The product rule · Investigation 17 of 100
The product rule: investigate a sign-changing linear factor with linear shift a = 0.5; exponential rate b = 0.75.
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The product rule · Investigation 18 of 100
The product rule: investigate two negative parameters with linear shift a = -1; exponential rate b = -0.5.
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The product rule · Investigation 19 of 100
The product rule: investigate a mild exponential influence with linear shift a = 1.5; exponential rate b = 0.25.
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The product rule · Investigation 20 of 100
The product rule: investigate a shallow decay with a zero crossing with linear shift a = -0.5; exponential rate b = -0.25.
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