4.7)My professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text. Right- and left-hand derivativesLet f (x) = |x|. (a) Calculate the right-hand derivatives of f (x) at x = 0. (b) Calculate the left-hand derivativeof f (x) at x = 0. (c) Does f (x) have a derivative at x = 0? (d) Illustrate the conclusions in (a), (b), and (c)from a graph.4.7.h=1limh→0+ hf(h) – f(0)(a) f:(0)= limh→0+= limh%3|hh→0+since |h| =-h for h> 0.f(h) – f(0)|h-0lim-h(b) f'(0) = limh→0-= lim1hh→0- h h→0- hsince |h| =-h for h < 0.(c) No. The derivative at 0 does not exist if the right- and left-hand derivatives are unequal.(d) The required graph is shown in Figure 4.8. Note that theslopes of the lines y = x and y = -x are 1 and -1, respec-tively, representing the right- and left-hand derivatives atx = 0. However, the derivative at x = 0 does not exist.Figure 4.8

Answered: Image /qna-images/answer/2a5df844-6c47-4a89-9db3-831a334cc454.jpg

Right- and left-hand derivatives Let f (x) = |x|. (a) Calculate the right-hand derivatives of f(x) at x = 0. (b) Calculate the left-hand derivative of f (x) at x = 0. (c) Does f (x) have a derivative at x = 0? (d) Illustrate the conclusions in (a), (b), and (c) 4.7. from a graph.

Right- and left-hand derivatives Let f (x) = |x|. (a) Calculate the right-hand derivatives of f(x) at x = 0. (b) Calculate the left-hand derivative of f (x) at x = 0. (c) Does f (x) have a derivative at x = 0? (d) Illustrate the conclusions in (a), (b), and (c) 4.7. from a graph.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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4.7)My professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.

Right- and left-hand derivatives
Let f (x) = |x|. (a) Calculate the right-hand derivatives of f (x) at x = 0. (b) Calculate the left-hand derivative
of f (x) at x = 0. (c) Does f (x) have a derivative at x = 0? (d) Illustrate the conclusions in (a), (b), and (c)
from a graph.
4.7.
h
=1
lim
h→0+ h
f(h) – f(0)
(a) f:(0)= lim
h→0+
= lim
h
%3|
h
h→0+
since |h| =-h for h> 0.
f(h) – f(0)
|h-0
lim
-h
(b) f'(0) = lim
h→0-
= lim
1
h
h→0- h h→0- h
since |h| =-h for h < 0.
(c) No. The derivative at 0 does not exist if the right- and left-
hand derivatives are unequal.
(d) The required graph is shown in Figure 4.8. Note that the
slopes of the lines y = x and y = -x are 1 and -1, respec-
tively, representing the right- and left-hand derivatives at
x = 0. However, the derivative at x = 0 does not exist.
Figure 4.8

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