3 ms·

"Easy as anything in math"? Now that's "obviously false hyperbole". You can't just brush away that discontinuity, specially when it's on the minimum (which is w

• thaumasiotes 13y ago
  You'll learn to take the derivative of |x| in high school calculus, shortly after learning how to take derivatives in general. It's not complex, and the fact that it's not defined at the origin doesn't mean there's a problem in taking it; it just means the function behaves "badly" there. I don't understand the focus on the discontinuity anyway; in working with the function, I'd be more concerned about the fact that it's piecewise defined. Consider a variant on the absolute value function: f(x) = x (when x >= 0); sin x (when x <= 0) It and its first and second derivatives are all continuous (after which it comes apart at the origin), but if you were working with the derivative, even though it's differentiable everywhere, you'd have to constantly be aware of whether the origin was in your domain. The great advantage of working with x^2 instead is that it behaves the same way everywhere, not that its derivative is continuous.
• thaumasiotes 13y ago
  This occurred to me after the editing window for my other reply passed, but... The tangent function has discontinuities at x = pi/2 and every interval of pi from it. When taking the derivative, is it more fruitful to say "you can't just brush away those discontinuities", or "sec^2 x"? And this is a derivative all calculus students are required to know!