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

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4 Let F X 3x X 2x 11 A Show That The Equation F X 0 Has A Unique Root A In 2 1 B Find The Newton S 1 (25.88 KiB) Viewed 25 times

4. Let f(x)=-3x - x? + 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. [Give the formula in the form x g(x-1) where g(x-1) and h(x-1) are polynomial functions.] h(x-1) (c) Show that the sequence obtained by the iterative formula in (b) will converge to a for any initial guess x, in (-2, -1]. (d) Hence, with x, =-1.5, estimate the value of a correct to 4 decimal places.