Question: Given the formula f(x) = x2 + 8x 12 (a) Determine the maximum and the corresponding value of x for this function analytically (i.e.,

Given the formula f(x) = −x2 + 8x − 12

(a) Determine the maximum and the corresponding value of x for this function analytically (i.e., using differentiation).
(b) Verify that Eq. (7.10) yields the same results based on initial guesses of x₁ = 0, x₂ = 2, and x₃ = 6.

Equation (7.10)

X4 = x2 - 1 (x-x) [f(x2) - f(x3)] (x2 - x3)

X4 = x2 - 1 (x-x) [f(x2) - f(x3)] (x2 - x3) [(x) - f (x)] - 2 (x-x) [f(x) - f(x3)] (xx3) [f(x) - f(x)] -

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