Question

The graph of f(x) with a domain of [-3,3] is composed of line segments as seen in the graph below (attached)

a.find f'(x) and sketch the graph. (ill sketch the graph, just need help finding f'(x))
b. Name the x-coordinate for each point of discontinuity of f'(x) over (-3,3)

Answer 1

if you have a line segment y= mx + b
the derivative is y'= m
in other words, dy/dx is the slope of the line.
in your case, you can find the slope of each line segment using change in y divided by change in x

Answer 2

you will get a discontinuity where each line segment meets (and the slope changes)

Answer 3

ok the slope of each line is:
1st line- -1/-1
2nd- -5/3
3rd- 5/2

Answer 4

you can simplify the slope of the first line to 1

Answer 5

I get confused on how to graph f'(x), which is the slope of each line right?

Answer 6

think of f'(x) as "y"
you have 3 equations: y= 1
y= -5/3
y= 5/2

Answer 7

ok so what about x? that's what I don't understand. how do you only graph y?

Answer 8

the slope y=1 is only true for the interval x=-3 to -2

Answer 9

ok

Answer 10

im sorry I still don't really understand. this is an open ended question so it makes it even worse.