g(x)=2x3−6x2+3g(x) = 2x^3 - 6x^2 + 3g(x)=2x3−6x2+3
Show that g(x)g(x)g(x) has a root between 0.8 and 0.9
Show that the equation g(x)=0g(x) = 0g(x)=0 can be written in the form x=36−2x\displaystyle x = \sqrt{\frac{3}{6-2x}}x=6−2x3
Use the iteration formula xn+1=36−2xn\displaystyle x_{n+1} = \sqrt{\frac{3}{6-2x_n}}xn+1=6−2xn3 with x0=0.8x_0 = 0.8x0=0.8 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, prove that α=0.832\alpha = 0.832α=0.832 to 3 decimal places
