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Find the differential equation of all tangent lines of the parabola y=x^2
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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?
All tangent lines? The parabola has a domain from -\(\infty\) to \(\infty\) lol!
Did you mean tangent line to that parabola at a specific x input or coordinate?
I realize this is differential equations and whatnot, but it doesn't seem to be a logical question IMHO. (thinking visually here)
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