Newtons method quessy 2002 HSC (1 Viewer)

[Cerebral]

I) Show that f(x) = e^x - 3x^2 has a root between x = 3.7 and x = 3.8.

II) Starting with x = 3.8 use one application of Newtons to find a better approximation for this root.

 

[Slidey]

I) show that the sign changes from f(3.7) to f(3.8)
II) x_2=x_1-f(x_1)/f'(x_1)
Better estimate=new x=3.8-f(3.8)/f'(3.8)

Recalling f'(x)=e^x-6x