Tangent and derivative
Tangent and derivative is an interactive experiment in Derivatives & Tangents, a free simulation from StudyFi Lab that runs right in your browser.
Drag the point along the graph of f. The dashed line is the tangent: it touches the curve at x₀ and has the slope k = f′(x₀). The lower graph collects these slopes for every x – that is the derivative f′(x). Where f rises, f′ is positive; where it falls, f′ is negative.
Try this: Pick the cubic and move the point to where the tangent is horizontal. What value does f′ show there, and where does the lower graph cross the x-axis?
Frequently asked questions
What does the “Tangent and derivative” experiment show?
Drag the point along the graph of f. The dashed line is the tangent: it touches the curve at x₀ and has the slope k = f′(x₀). The lower graph collects these slopes for every x – that is the derivative f′(x). Where f rises, f′ is positive; where it falls, f′ is negative.
How do I try “Tangent and derivative”?
Pick the cubic and move the point to where the tangent is horizontal. What value does f′ show there, and where does the lower graph cross the x-axis?
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