Given the graph of the function f(x) construct the slope field to sketch the graph of the anti derivative F(x) that passes through the point (0,-1)
Stacey Warren - Expert brainly.com
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@skay here is what we do. We draw a graph with x and y the top graph is the slope, the number you pick off is the slope, so at x=0, the slope is zero a line with a slope of zero is a horizontal line. We sketch in the start of a set of lines with a slope of zero along the y-axis.
then at x=1, the slope is 1, that is a 45 degree line
we put in a little piece of line at 45 degrees|dw:1377859155775:dw|
at x = 2 slope is still 1,
I'm going to shift the little segments up so we can fill in the cures later
back to a slope of zero at x=3
down to a slope of -1,
I can't quite tell what x is there
a slope of -1 is a 45 degree line going down
and back to zero
then you connect the segments with smooth curves, it would look something like what is on the whiteboard. Then you go back and pick of the line that goes through (0,-1)
Ok I just drew it again, so its a bit clearer.
then you pick off the line that goes through the point (0,-1)
and put that on it's own graph,
it would look something like that, you can probably do a better graph on your paper.lol that is it:)
that is the anti-derivative F(x) that goes through (0,-1)
Hope I helped you! :D
all your doing is making a graph that has the correct slope at each x location.