Problem #3: Consider the set C'([a, b), the set of differentiable functions (that is, we takethe set of all functions f : [a, b] → R so that f' is well defined). Show that this set forms avector space over R. [This means you must explain why: 1) the sum f + g of two functionsf,g in this set is still in the set, and 2) the scalar multiple cf of any function f in this setis still in the set, for any c in R and 3) the function f (x) = 0 is in the set. You may find ithelpful to use properties of derivatives that you studied once upon a time in calculus!

Given C1[a,b] is the set of all differentiable functions. We need to show that f+g is in C1[a,b]…

Problem #3: Consider the set C'([a, b]), the set of differentiable functions (that is, we take the set of all functions f : [a, b] → R so that f' is well defined). Show that this set forms a vector space over R. [This means you must explain why: 1) the sum f + f,g in this set is still in the set, and 2) the scalar multiple cf of any function f in this set is still in the set, for any c in R and 3) the function f(x) = 0 is in the set. You may find it helpful to use properties of derivatives that you studied once upon a time in calculus!] of two functions

Problem #3: Consider the set C'([a, b]), the set of differentiable functions (that is, we take the set of all functions f : [a, b] → R so that f' is well defined). Show that this set forms a vector space over R. [This means you must explain why: 1) the sum f + f,g in this set is still in the set, and 2) the scalar multiple cf of any function f in this set is still in the set, for any c in R and 3) the function f(x) = 0 is in the set. You may find it helpful to use properties of derivatives that you studied once upon a time in calculus!] of two functions

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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