4. Let f(x)=-3x4 – x² + 2x +11. (a) Show that the equation f(x) = 0 has a unique root a in (-2,-1]. (b) Find the Newton'

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4 Let F X 3x4 X 2x 11 A Show That The Equation F X 0 Has A Unique Root A In 2 1 B Find The Newton 1 (68.77 KiB) Viewed 21 times

4. Let f(x)=-3x4 – x² + 2x +11. (a) Show that the equation f(x) = 0 has a unique root a in (-2,-1]. (b) Find the Newton's iterative formula for solving the equation f(x)= 0. g(x,-1) [Give the formula in the form x, where g(x,-1) and h(x,-1) are polynomial functions.] = n- n- h(x,-1) (c) Show that the sequence obtained by the iterative formula in (b) will converge to a for any in (-2,-1]. initial guess x, (d) Hence, with x, =-1.5, estimate the value of a correct to 4 decimal places. =