(a) Suppose that the tangent line to the curve y = f (x) at the point...

(a)

Suppose that the tangent line to the curve y = f (x) at the point (−9, 53) has equation y = −1 − 6x. If Newton's method is used to locate a root of the equation f (x) = 0 and the initial approximation is x₁ = −9, find the second approximation x₂.

(b)

Suppose that Newton's method is used to locate a root of the equation f (x) = 0 with initial approximation x₁ = 9. If the second approximation is found to be x₂ = −2, and the tangent line to f (x) at x = 9 passes through the point (17, 6), find f (9).

(c)

Use Newton's method with initial approximation x₁ = 2 to find x₂, the second approximation to the root of the equation x³ = 6x + 6.

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Expert Solution

milcah answered 1 year ago

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