"Calculus of polynomials can be really simple by thinking of them as nothing more than instructions for building n-dimensional cuboids. Half of their boundaries correspond to the first derivative, and their share of half the boundaries of the cuboid of dimension n+1 is the antiderivative. x³ has six boundaries x². Therefore, the derivative of f(x) = x³ is f'(x) = 3x². x⁴ has eight boundaries x³. The antiderivative of f(x) is thus F(x) = x⁴/4."
The LEGO cuboid represents f(x)=x³ (blue cube) + 3x² (red cuboid) + -1x² (white cuboid) + 3*-1x (white cuboid), That's f(x) = x³ + (3-1)x² - 3x = x³ + 2x² - 3x. This equals (x+0)(x+3)(x-1). Backwards, left and down are negatively connoted with a minus sign. The 1st derivative equals half of the cuboid's boundaries. f'(x) = 3x12 (blue squares) +2*3x (two red rectangles) - 2*-1x (two white rectangles) -3x (white rectangle).
Curves drawn with this ingenious tool/toy: https://www.matheretter.de/rechner/gfplot Calculus of f(x)=x³+2x²-3x (blue graph), f'(x) = 3x² + 4x -3, pink, f''(x) = 6x +4, turquoise, f'''(x) = 6, green, F(x) = x⁴/3 +2x³/3 + 3x²/2 +c, purple (c = 0)
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#Calculus of #polynomials could also be really simple. I hope you'll enjoy lazybones's darling;)
Polynomials:
n-dimensional cuboids.
Epsilon, fuck off!
