Syllabus

·           Derivatives

·           One-sided derivative of functions at a point and examples

·           Derivability and continuity properties of derivative

·           Chain rule

·           Darboux theorem

·           Intermediate value theorem for derivatives

·           Rolle's theorems

·           Lagrange mean value theorem

·           Cauchy's mean value theorem

·           Taylor's theorem and Maclaurin's theorem

·           Extreme value theorem: necessary condition for local extrema

·           First derivative test for extrema

·           Taylor's polynomials and its examples

·           Remainder in Taylor series

·           L'Hospital's Rule and other indeterminate forms