Question

How the heck do you make a slope field?

Answer 1

Draw the coordinate axes and the point (2,8).

Answer 2

Taking x = 2, evaluate the given derivative. (Note: I'm having trouble reading the definition of this derivative.)

Answer 3

Is this it?\[\frac{ dy }{ dx }=x*\sqrt[3]{y}?\]

Answer 4

Yes, that is the equation.

Answer 5

Just evaluate this derivative at (2,8).

Answer 6

So we plug in 2 and 8 in the equation? 2 * 2 = 4?

Answer 7

Exactly. The point is, the slope of the tangent line to the SOLUTION y=f(x) is 4 when you're at (2,8).

Answer 8

going back to the previous graph, draw a slope of +4 there (at (2,8)).