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1yand y 36 16xX

Question

Use Newton's method to approximate all intersection points of the following pair of curves.

Round to six decimal places as needed.

1
yand y 36 16x
X
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1 yand y 36 16x X

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Step 1

Before we get into the solution of the question, let's understand a bit about Newton's method. 

If xn is an approximate solution of F(x) and F’(xn) ≠ 0 then the next approximate solution, xn+1  is given by the expression on the White Board.

F(x
,)
х, — х,
'n+1
F'(x
п
п-1
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F(x ,) х, — х, 'n+1 F'(x п п-1

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Step 2
Step 3

Based on the pair of curves given to us, let's define F(x) as:

F(x) = 1/x – (36 – 16x2)  = 16x2 - 36 + 1 /x

Hence, F'(x) = 32...

F(x,)
F(x
п+1
71
16х? — 36 +1/х
п+1
72
32х —1/x2
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F(x,) F(x п+1 71 16х? — 36 +1/х п+1 72 32х —1/x2

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Tagged in

Math

Calculus

Derivative

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