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.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

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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