Question: (5)Let f be the function defined by f(x) =x x 3 . (a)Show that the equation f(x) =4 has a solution in the interval [0,4].

(5)Let f be the function defined by f(x) =xx3 .

(a)Show that the equation f(x) =4 has a solution in the interval [0,4].

(b)Let's denote the solution above by r.Is it possible to approximate r using Newton's method with initial approximation x1= 1?Justify your answer.(c)Using Newton's method, find the 2nd approximation of r with initial approximation x1= 2.

(6)UsingNewton'smethod,findthe2nd approximationofthe x-coordinateofthe intersectionofthecurves y=(x+ 1)(x3)and y=4x1,withinitial approximation x1= 5

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