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 it

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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 It 1 (20.67 KiB) Viewed 27 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 , where g(x-1) and h(x...) are polynomial functions.) h(x) (e) 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. (25 marks)