Question

Calculus help

Answer 1

@AloneS

Answer 2

What do you notice about the overall shape of the slope field, what kind of function does it look like?

Answer 3

Im not sure. parabola?

Answer 4

@mrm

Answer 5

@freckles

Answer 6

A slope field describes the general solution to a first order differential equation. That means that if you draw a line that flows through the slope lines, you'll get the general shape of the solution. There are an infinite number of them that you can draw (hence why there are an infinite number of exact solutions for every general solution to a Diff Eq)

Answer 7

Ok. I dont know how to do it since the options arent in dy/dx form.

Answer 8

The solution to a 1st order DE will be in y=f(x) form, not differential form. The general shapes within the slope field will give you an idea of what kind of function is your general solution. I think you're on the right track with parabola. Options C and D are what kind of functions?

Answer 9

So lets look closer. For a parabola, you would expect all general parabolas (no y intercept added) to intersect at the origin, correct?

Answer 10

And it looks like we have asymptotes at y=x and y=-x. Do parabolas have asymptotes on those lines?

Answer 11

no?

Answer 12

Right. Parabolas don't have asymptotes. So we can rule out parabolas, options A and B are both parabolic functions.

Answer 13

ohhh ok!

Answer 14

Do you see the general shape of the slope field? It should look like this to you.