Question

The set C1 [a, b] of functions which have continuous first derivative on [a, b]. View C1 [a, b] as a subset of C[a, b].

a) True
b) False

Answer 1

The set C1 [a, b] of functions which have continuous first derivative on [a, b] is a subset of C[a, b].

Step-by-step explanation:

True. The set C1 [a, b] consists of functions that have continuous first derivatives on the interval [a, b]. This means that the functions in C1 [a, b] are not only continuous, but their derivatives are also continuous. Since the set C1 [a, b] is a subset of C[a, b], which represents the set of all continuous functions on [a, b], it is true that C1 [a, b] is a subset of C[a, b].