From secant to tangent
From secant to tangent is an interactive experiment in Derivatives & Tangents, a free simulation from StudyFi Lab that runs right in your browser.
A secant passes through two points of the graph, x₀ and x₀ + h. Its slope is the difference quotient k(h) = (f(x₀ + h) − f(x₀)) / h. As h gets smaller, the second point slides towards the first and the secant turns into the tangent: the limit of k(h) for h → 0 is the derivative f′(x₀).
Try this: Let h shrink towards 0 (with the slider or the animation) and watch the secant slope in the values close in on f′(x₀). Try it with the sine as well.
Frequently asked questions
What does the “From secant to tangent” experiment show?
A secant passes through two points of the graph, x₀ and x₀ + h. Its slope is the difference quotient k(h) = (f(x₀ + h) − f(x₀)) / h. As h gets smaller, the second point slides towards the first and the secant turns into the tangent: the limit of k(h) for h → 0 is the derivative f′(x₀).
How do I try “From secant to tangent”?
Let h shrink towards 0 (with the slider or the animation) and watch the secant slope in the values close in on f′(x₀). Try it with the sine as well.
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