INTERACTIVE DEMO: CALCULUS

Experience how Artichoke peels back the layers of understanding. Master each layer to unlock the next.

1
The Foundation - Rates of Change
Understand how things change in everyday life

Before diving into derivatives, we must understand rates of change. A car's speedometer shows rate of change of position. A thermometer shows rate of change of temperature.

f(x)
Δ
t

Interactive 3D Visualization

A car travels 120 miles in 2 hours. What is its average rate of change (speed)?

A) 120 mph
B) 60 mph
C) 240 mph
2
Slope as Instantaneous Rate
Connect slopes to the concept of derivatives
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The slope of a curve at any point is the instantaneous rate of change. This is the foundation of the derivative!

f'(x) = lim[h→0] (f(x+h) - f(x))/h

The Definition of a Derivative

What does f'(x) represent?

A) Instantaneous rate of change
B) Average rate of change
C) Total change
3
The Power Rule
Master the most essential differentiation technique
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4
Chain Rule & Composition
Handle complex nested functions
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5
The Heart - Applied Derivatives
Real-world optimization and related rates
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