Lecture

Derivable ↔ Differentiable

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Description

This lecture covers the concept of a function being derivable if and only if it is differentiable, demonstrating the equivalence through a step-by-step proof. It explores the conditions for a function to be differentiable at a point, using examples like sin(x) at x=0.

In MOOCs (2)

Analysis I (part 5): Continuous and derivable functions, the derivative function

This brings us to the heart of our discussion of functions: the concept of the derivability of a function. We are particularly interested in the question of the continuity of derived functions. We begin the chapter by completing the study of continuous functions by studying their properties on closed intervals. This enables us to define the maximum and minimum of continuous functions. We go on to define the bisection method, and demonstrate it. Introducing the concepts of maximum and minimum allows us to

Analysis I

This course covers : Part 1: Prelude, basic concepts, real numbers. Part 2: Introduction to complex numbers. Part 3: Real number sequences I and II. Part 4: Limit of a function, continuous functions. Part 5: Continuous functions and derivable functions, the derivative function. Part 6: Studies of functions, limited developments. Part 7: Indefinite and definite integrals, integration (selected chapters).

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