Show that the equation x3+8x=4x^3 + 8x = 4x3+8x=4 has a solution between x=0x = 0x=0 and x=1x = 1x=1.
Show that the equation x3+8x=4x^3 + 8x = 4x3+8x=4 can be rearranged to give: x=12−x38\displaystyle x = \frac{1}{2} - \frac{x^3}{8}x=21−8x3
Starting with x0=0x_0 = 0x0=0, use the iteration formula xn+1=12−xn38\displaystyle x_{n+1} = \frac{1}{2} - \frac{x_n^3}{8}xn+1=21−8xn3 twice to find an estimate for the solution to x3+8x=4x^3 + 8x = 4x3+8x=4.