Question

Find the differential equation of all tangent lines of the parabola y=x^2

Answer 1

My guess: y=x^2
The derivative of this function is the slope of its tangent line,
so: y'=2x --> slope of the tangent line

y=mx+b
Since y =x^2, and m=y'
x^2=y'x+b
Differentiating wrt x will give:
2x=y'+xy'' ---> answer

Is that right?

Answer 2

All tangent lines? The parabola has a domain from -\(\infty\) to \(\infty\) lol!

Answer 3

Did you mean tangent line to that parabola at a specific x input or coordinate?

Answer 4

I realize this is differential equations and whatnot, but it doesn't seem to be a logical question IMHO. (thinking visually here)