The function where the bisection method is implemented shouldhave the following

Question

The function where the bisection method is implemented shouldhave the following parameters and should return the followingvalue. The input parameters are:    -a function f whose root we want tocompute    -a and b are the left and right endpoint ofthe interval where a root of f we want to compute. This      interval should contain only one sucha root. If there are no roots in this interval, the programshould      stop and print the error message: "Noroots found."    -epsilon (=acceptable error) which should beset by the user (should be less then 1.0 but larger       than 0.0) The function should implement the following algorithm. Letf_a=f(a) and f_b=f(b) 1. Compute the funtion value at the midpoint of the interval(a and b are the endpoints of the interval). The midpoint iscomputed as (a+b)/2. 2.If f_mid is zero, the midpoint is the root. REturn theroot. 3.If f_mid is not zero and    a.) if f_mid*f_a<0.0, replace b with themidpoint    b.) if f_mid*f_b<0.0, replace a with themidpoint. 4. Repeat steps 1-3 in a while loop until the distance betweena and b is less then epsilon by using the function fabs (a-b) tofind the distance between a and b. Return midpoint of final interval as the root. Use this runction whose roots we are to compute: 3x^3-3x^2+0.2 (Although is has three roots, we are interested in roots inthese two intervals: [-1, 0] and [0, 0.5] The function where the bisection method is implemented shouldhave the following parameters and should return the followingvalue. The input parameters are:    -a function f whose root we want tocompute    -a and b are the left and right endpoint ofthe interval where a root of f we want to compute. This      interval should contain only one sucha root. If there are no roots in this interval, the programshould      stop and print the error message: "Noroots found."    -epsilon (=acceptable error) which should beset by the user (should be less then 1.0 but larger       than 0.0) The function should implement the following algorithm. Letf_a=f(a) and f_b=f(b) 1. Compute the funtion value at the midpoint of the interval(a and b are the endpoints of the interval). The midpoint iscomputed as (a+b)/2. 2.If f_mid is zero, the midpoint is the root. REturn theroot. 3.If f_mid is not zero and    a.) if f_mid*f_a<0.0, replace b with themidpoint    b.) if f_mid*f_b<0.0, replace a with themidpoint. 4. Repeat steps 1-3 in a while loop until the distance betweena and b is less then epsilon by using the function fabs (a-b) tofind the distance between a and b. Return midpoint of final interval as the root. Use this runction whose roots we are to compute: 3x^3-3x^2+0.2 (Although is has three roots, we are interested in roots inthese two intervals: [-1, 0] and [0, 0.5]

Explanation / Answer

Please rate! #include #include using namespace std; double equation(double x) {     return (3.0*pow(x,3) - 3.0*pow(x,2) +0.2);    } double bisection(double a, double b, double epsilon) {     double f_a, f_b, f_mid, mid;         while (fabs(a - b) > epsilon) {         mid = (a + b) / 2;         f_mid =equation(mid);         if (f_mid == 0.0) {            returnmid;         }         else {            f_a =equation(a);            f_b =equation(b);           if(f_mid*f_a < 0.0)              b = mid;           if(f_mid*f_b < 0.0)              a = mid;         }      }      return mid; } int main() {      double epsilon = 0.0001;                           cout

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