Dervatives and Newton's Method

#1. f(x) = x^4-17x^2+18

What is the relationship between the sign of f'(x) and the graph f(x) ?:eek:

What is the relationship between the roots of f''(x) and the graph of f(x) ?:eek:

What is the relationship between the sign of f''(x) and the graph of f(x) ?:eek:

#2. Given that f(x) = sin(x) use Newton's Method to find the first 2 positive zeros showing the first few approximations in each case.

So...

pi

___

x1: 3

x2: 3.142546543

x3: 3.141592653

x4: 3.14159255359

also...

2pi

____

x1: 6

x2: 6.29100619138

x3: 6.28310514772

x4: 6.28318530718

The first positive zero is: 3.14159

The second positive zero: 6.28319

What happens when you took pi/2 as first approximation? Explain

I got 1 but else is there to say:eek: :eek:

#3. if f(x) = x^4-17x^2+18

f''(x) = 12x^2-34

Therefore f''(x) = 0 if x = -sqrt(102)/6 and sqrt(102)/6 and these are the x-coordinates of the points of __:eek: ___ of f(x)?

Thanks for the Help!