1) Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. 2 x − x2 + 1 = 0, x1 = 2
What is x3 =?
2) Use Newton's method to find all solutions of the equation correct to six decimal places.
x + 4 = x^2 - x
What is X =?
3) Use Newton's method to find all solutions of the equation correct to six decimal places.
5 cos(x) = x + 1
What is X =?
4) A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.
5A) Use Newton's method to find the critical numbers of the function
f(x) = x6 ? x4 + 3x3 ? 4x
What is X =?
B) Find the absolute minimum value of f correct to four decimal places.

Check below, please

Step-by-step explanation:

Hello!

1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

2)  Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.

We can rewrite it as:

As for

3) Rewriting and calculating its derivative. Remember to do it, in radians.

For the second root, let's try -1.5

For x=-3.9, last root.

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.

For -1.2

For x=0.4

and for x=-0.4

These roots (in bold) are the critical numbers

i dont know sorry

step-by-step explanation: