Definition: Let f: A → R be a function defined on a set A containing the point c. We say that fis differentiable at c (or has a derivative f'(c) at c) if the limit below exist and is finite f'(c) = lim X→C f(x) = f(c) X-C We say that f is differentiable S≤ A iff f'(c) exists for all c E S. The function f': S → R is called the derivative of f on S. 1 a) f(x) = √√, x > 0 b) f(x) = √√x, x ≥ 0 Use the definition above to find the derivative of each function and determine the subset of its domain at which the derivative f' exists.
Definition: Let f: A → R be a function defined on a set A containing the point c. We say that fis differentiable at c (or has a derivative f'(c) at c) if the limit below exist and is finite f'(c) = lim X→C f(x) = f(c) X-C We say that f is differentiable S≤ A iff f'(c) exists for all c E S. The function f': S → R is called the derivative of f on S. 1 a) f(x) = √√, x > 0 b) f(x) = √√x, x ≥ 0 Use the definition above to find the derivative of each function and determine the subset of its domain at which the derivative f' exists.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please explain clearly how you determine the subset at which the derivative exists
Transcribed Image Text:Definition: Let f: A → R be a function defined on a set A containing the point c. We say that f is
differentiable at c (or has a derivative f'(c) at c) if the limit below exist and is finite
ƒ'(c) = lim
X→C
f(x) − ƒ(c)
X-C
We say that f is differentiable S ≤ A iff f'(c) exists for all c E S. The function f':S → R is called the
derivative off on S.
1
a) f(x) =,x>0
b) f(x)=√x,x ≥0
Use the definition above to find the derivative of each function and determine the subset of its
domain at which the derivative f' exists.
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