Continuity and Differentiability
Key points
- Continuity of a function- a function that does not have any abrupt changes in its values
- A differential function is a function whose derivative exists at a certain point
Continuity of a function is when a function is not subject to any small change in its values.
- Discontinuous functions are functions that have a value that does not actually exist
- This is often represented on a graph through an open dot
A function is differentiable when it has a derivative at any given point
- Derivatives are the slope of a curve at a certain point
- Because the slopes of a curve are constantly changing, the derivative/slope of the curve can be found by finding the slope of the tangent line to any given point
Formula Booklet
- Derivatives will be expressed as the change in x over the change in y
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