Theory?

Calculus Level 3

Which statements below are true?

a) There exists a continuous function $f:\mathbb{R} \rightarrow \mathbb{R}$ such that it is not differentiable at any point.

b) If a complex-valued function $f:\mathbb{C} \rightarrow \mathbb{C}$ has a first derivative, then it is infinitely derivative.

a)True, b)True a)False, b)False a)True, b)False a) False, b)True

1 solution

Fiki Akbar
Mar 11, 2016

a. The function that continuous everywhere but differentiable nowhere is called Weierstrass function.

b. If the complex function is differentiable (has first complex derivative), than the function is holomorphic, hence analytic (infinitely differentiable).

Theory?

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