What is the main purpose of the Bisection Method?, To find the maximum of a function, To find a root of an equation, To find the derivative of a function, To find the area under a curve, What condition must f(a) and f(b) satisfy before using the Bisection Method?, They must have the same sign, They must both be zero, They must have opposite signs, They must be equal, How is the midpoint p1 calculated?, If f(P1)=0, what do we do?, Stop; P1 is the root, Choose a new interval randomly, Double the interval, Calculate the derivative, If a=2 and b=6, what is the midpoint P1?, 2, 3, 4, 8, Which of the following can be used as a stopping condition?, The error is smaller than the tolerance, The interval becomes larger, The function becomes more complicated, The midpoint is always negative, 9. In the Bisection Method, what does Pn represent?, The derivative of the function, The midpoint at iteration n, The initial value of a, The maximum error, What is the first step in the Bisection Method?, Calculate the derivative, Set a1=a and b1=b, Find the maximum value, Multiply a and b, Suppose we are applying the Bisection method on [2, 4]. We have f(2) = -8 and f(4) = 10. The midpoint is p1 = 3, where f(3) = -1. What is the new interval [a2, b2]for the second iteration?, [2,4], [3,4], [2,3], [-1,2], What happens to the interval after each successful Bisection step?, It becomes twice as large, It becomes half as large, It stays the same, It becomes zero
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