maths question please help me

Let f(x) = (e^x) - 3x , f '(x) = (e^x) - 3
Since f(0)*f(1) <0 and f(1)*f2) <0
There is one root in (0,1) and another in (1,2)

Using Newton's method with the formula

圖片參考：http://mathworld.wolfram.com/images/equations/NewtonsMethod/NumberedEquation5.gif


For the first root, let x0 = 0.5
n xn
0 0.5
1 0.610059655
2 0.618996779
3 0.619061283
4 0.619061286
5 0.619061286

For the second root, let x0 = 1.5
n xn
0 1.5
1 1.512358146
2 1.512134625
3 1.512134552
4 1.512134552
5 1.512134552

Hence x = 0.619061286 or x = 1.512134552 (9 d.p.)