Suppose that Newton's method is used to locate a root of the equation f ( x ) 0 with initial approximation x 1 5 If the second approximation is found to be x 2 1, and the tangent line to f ( x ) at x 5 passes through the point (20,4), find f (5) Use Newton's method with initial approximation x 1 7 to find x 2 , the second approximation to the root of the equation x 3 8 x 1

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Question: Suppose that Newton's method is used to locate a root of the equation f ( x ) = 0 with initial approximation x 1 =

Suppose that Newton's method is used to locate a root of the equation f(x) = 0 with initial approximation x₁ = 5. If the second approximation is found to be x₂ = 1, and the tangent line to f(x) at x = 5 passes through the point (20,4), find f(5).

Use Newton's method with initial approximation x₁= 7 to find x₂, the second approximation to the root of the equation x³ = 8x 1.

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