Question

Select the correct answer. Consider these equations: f(x)=
`x^(3)`+3 g(x)=
`x^(2)`+2 Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use this graph as a starting point.

Answer 1

A

Explanation:

The solution to these two graphs will be when they are equal. Therefore:

`x^3+3=x^2+2 \\\\x^3-x^2+1=0 \\\\x\approx -0.755\approx -(13)/(16)`

Hope this helps!

Answer 2

-13/16

Explanation:

f(x)=x^3+3

g(x)=x^2+2

We know the solution is around -1

x^3+3 = x^2 +2

Subtract x^2+2 from each side

x^3 -x^2 -1 = f(x)

We need to find the derivative

3x^2 -2x = f'(x)

Newtons method of successive approximation states

xn+1 = xn -f(xn) / f'(xn)

Function

x3−x2+1

Derivative

x⋅(3⋅x−2)

x

-0.75488

Iterations

Step x F(x) |x(i) - x(i-1)|

x1 -0.8 -0.152000 0.152000

x2 -0.75682 -0.006259 0.006259

x3 -0.75488 -0.000012 0.000012

The approximate answer is -0.75488

The closest answer given is -13/16