Question
Asked Feb 13, 2020
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these are notes from class, i was absent 

The right-sided and left-sided derivatives of a function at a point a are given by
Ay
10-
f(a + h) - f(a)
f(a + h)- f(a)
f, '(a) = lim
h 0+
limits exist. The derivative f'(a) exists if and only if f. '(a) =f_ '(a). Complete parts (a) through
(c) using f(x) = |2x+2| and a = - 1.
and f- (a) = lim
respectively, provided these
8-
h 0-
6-
%3D
4-
a. Sketch the function. Use the graphing tool to graph the function.
2-
Click to
10
8.
2.
-2
4
-4
-10
-8
-6
enlarge
graph
-2-
-4
-6
in
help_outline

Image Transcriptionclose

The right-sided and left-sided derivatives of a function at a point a are given by Ay 10- f(a + h) - f(a) f(a + h)- f(a) f, '(a) = lim h 0+ limits exist. The derivative f'(a) exists if and only if f. '(a) =f_ '(a). Complete parts (a) through (c) using f(x) = |2x+2| and a = - 1. and f- (a) = lim respectively, provided these 8- h 0- 6- %3D 4- a. Sketch the function. Use the graphing tool to graph the function. 2- Click to 10 8. 2. -2 4 -4 -10 -8 -6 enlarge graph -2- -4 -6 in

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Expert Answer

Step 1

Given function is f(x)= |2x+2|

a) We have to graph the function.

 

2x+2=0 

or, 2x=-2

or, x=-1

So at x=-1 there is vertex.

 

Step 2

Calculus homework question answer, step 2, image 1

Using this piecewise function we make two tables.

x -5 -4 -3 -2 -1
y 8 6 4 2 0

 

x 0 1 2 3 4
y 2 4 6 8 10
...

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Math

Calculus