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Consider the function \(f(x) = x^3 + 2x - 2\)

A student performs Newton's method beginning with initial guess \(x_0 = 1\):

1.  Which of the following is true?

a.  There is a mistake computing x₁

b.  The value x₁ is correct, but there is a mistake computing x₂

c.  The value x₂ is correct, but there is a mistake computing x₃

d.  The value x₃ is correct, but there is a mistake computing x₄

d.  There are no errors in this table.

2. Compute the antiderivative \(\int \cos x + 4x + 4 dx\)

a.  \(\sin x + 2x^2 + 4x + c\)

b.  \(\sin x + 2x^2 + c\)

c.  \(-\sin x + 4x^2 + 4x + c\)

d.  \(-\sin x + 4x^2 + c\)

d.  \(-\sin x + 2x^2 + 4x + c\)