3836.sagews

x = var('x')
y = var('y')

outside = Piecewise([[(0, 0.119), -8.00522809*x^2 + 2.798651832*x + 1.369663556],
                     [(0.119, 4.239), 1.020728214 - 0.262606257*ln(x)]])
                     
inside = Piecewise([[(0, 0.07371368), 28.82379954*x^2 - 4.249303053*x + 1.321736529],
                    [(0.07371368, 3.407), 0.0712696786*x^2 - 0.4614920586*x + 1.19875589],
                    [(3.407, 4.239), 1.020728214 -0.262606257*ln(x)-0.119]])
bell = [plot(outside, xmin=0, xmax=4.239, ymin = 0, ymax = 4.239, gridlines = True ),
        plot(inside, xmin=0, xmax=4.239, ymin = 0, ymax = 4.239, gridlines = True ),
        plot(line([(3.407,inside(3.4069)),(3.407,outside(3.407)-.119)]), xmin = 0, xmax = 4.239, ymin = 0, ymax = 4.239, gridlines = True)]

p = sum(bell)
p.show()

inside

\newcommand{\Bold}[1]{\mathbf{#1}}$$\begin{cases} 28.8237995400000 \, x^{2} - 4.24930305300000 \, x + 1.32173652900000 &\text{on $(0, 0.0737136800000000)$}\cr 0.0712696786000000 \, x^{2} - 0.461492058600000 \, x + 1.19875589000000 &\text{on $(0.0737136800000000, 4.23900000000000)$}\cr \end{cases}$$

outside

\newcommand{\Bold}[1]{\mathbf{#1}}$$\begin{cases} -8.00522809000000 \, x^{2} + 2.79865183200000 \, x + 1.36966355600000 &\text{on $(0, 0.119000000000000)$}\cr -0.262606257000000 \, \log\left(x\right) + 1.02072821400000 &\text{on $(0.119000000000000, 4.23900000000000)$}\cr \end{cases}$$