please help me answer this question

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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2. If f is a function and c is some point in the domain of f, define
f(c+ h) – f(c – h)
f(c) = lim
h→0
2h
Compute f(2) when f(x) = 1/x. Show that f(2) = f'(2). (You do not need to find
(i)
f' (x) by first principles.)
Show that f(x) = f'(x) for all x E R when f (x) = x². (You do not need to find f'(x)
(ii)
by first principles.)
(iii)
f.
Compute the value of f(0) when f(x) = |x|. Explain why f cannot be the derivative of
Transcribed Image Text:2. If f is a function and c is some point in the domain of f, define f(c+ h) – f(c – h) f(c) = lim h→0 2h Compute f(2) when f(x) = 1/x. Show that f(2) = f'(2). (You do not need to find (i) f' (x) by first principles.) Show that f(x) = f'(x) for all x E R when f (x) = x². (You do not need to find f'(x) (ii) by first principles.) (iii) f. Compute the value of f(0) when f(x) = |x|. Explain why f cannot be the derivative of
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