d) Now, recall our class discussions relative to transformations of graphs and explain what is the connection between the graph of y = |=| and y = |z - 31. What is the critical point of this new function, y= z - 317 Explain.

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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1. a) From our class discussions, recall that the derivative of a function f at a is, by definition,
f(a) = lim
f(a + h) – f(a)
h
provided that this limit exists.
Apply this definition to find the derivative of f(z) =r² - 3 at a = 6.
b) Check your answer from a) by applying classic rules of differentiation.
2. Consider the absolute value function which is formally defined as
z, if z20
f(2) = \=| ={-z,if z<0
a) Sketch the graph of f(2) - Jz|. Is this function continuous at 0? What about diferentiable
at 0? Explain.
b) What is the only critical point of y = |z|? Explain.
Recall that a critical point is, by definition, a point for uhich it is either the case that f'(x) = 0
or that the derivative does not ezist.
c) Sketch the graph of y= f'(2).
d) Now, recall our class discussions relative to transformations of graphs and explain what
is the connection between the graph of y= |z| and y = |z-31. What is the critical point of this
new function, y = |z – 3|? Explain.
Transcribed Image Text:1. a) From our class discussions, recall that the derivative of a function f at a is, by definition, f(a) = lim f(a + h) – f(a) h provided that this limit exists. Apply this definition to find the derivative of f(z) =r² - 3 at a = 6. b) Check your answer from a) by applying classic rules of differentiation. 2. Consider the absolute value function which is formally defined as z, if z20 f(2) = \=| ={-z,if z<0 a) Sketch the graph of f(2) - Jz|. Is this function continuous at 0? What about diferentiable at 0? Explain. b) What is the only critical point of y = |z|? Explain. Recall that a critical point is, by definition, a point for uhich it is either the case that f'(x) = 0 or that the derivative does not ezist. c) Sketch the graph of y= f'(2). d) Now, recall our class discussions relative to transformations of graphs and explain what is the connection between the graph of y= |z| and y = |z-31. What is the critical point of this new function, y = |z – 3|? Explain.
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