Calculus › Section C · Derivatives › Topic C.1
The derivative and the tangent line
One limit captures both the slope of a tangent line and the speed of anything that changes. That limit is the derivative, and it is the engine of the entire first half of this course.
In this topic
- From one point to every point
- The definition
- Worked example: the derivative of x²
- Worked example: the derivative of 1/x
- Costumes: an equivalent form and the notations
- Reading the derivative off a graph
- Worked example: a growth rate with units
- Where derivatives fail
- Differentiable means continuous
- Estimating derivatives from data
- Common mistakes to avoid
- Key takeaways
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Standards: 2