Summary
Equations of tangent and normal
- change between increasing and decreasing -> 1st derivative test
- change of concavity -> 2nd derivative test
- using chain rule
L’Hôpital’s rule
- applies to limits at infinity and one-sided limits
provided the right limit exists or equals infinity/negative infinity
Concept
Increasing and decreasing
Critical points
not including the endpoints of the interval
Indeterminate forms
Rolle’s theorem
- if the endpoints over an interval are the same, then there is a local minimum/maximum in the interval
Mean value theorem
- there is a point whose gradient is average gradient between the endpoints
Application
Critical points, minima and maxima of piecewise funtions
not all continuous points are differentiable
Deriving the mean value theorem from Rolle’s theorem