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. = 2. (a) Create a program in R which approximates the root of f(x) = x3 7x2 +14x 6 between 0 and 1 using the interval bisection method. Graph the function first to find the starting interval. Use the absolute convergence criterion with = 0.01. Provide the R code and show the approximation corresponding to the first five iterations. (b) Repeat (a) using the R function uniroot with the same starting interval and = 0.01. Compare convergence of uniroot and the bisection method. How many iterations did it take for each of the methods to converge if = 0.01? When = 0.01, which method found a solution x* where f(x*) is closest to 0? a . = 2. (a) Create a program in R which approximates the root of f(x) = x3 7x2 +14x 6 between 0 and 1 using the interval bisection method. Graph the function first to find the starting interval. Use the absolute convergence criterion with = 0.01. Provide the R code and show the approximation corresponding to the first five iterations. (b) Repeat (a) using the R function uniroot with the same starting interval and = 0.01. Compare convergence of uniroot and the bisection method. How many iterations did it take for each of the methods to converge if = 0.01? When = 0.01, which method found a solution x* where f(x*) is closest to 0? a

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