Figure out the corresponding recursion, and then design and code an algorithm in Matlab.

The bisection method for finding roots of functions is based on the following idea: Suppose f is a continuous function on (at least) the interval [a,b], and that f(a) and f(b) differ in sign. Then by the Intermediate Value Theorem, f has at least one root between a and b. To find that root, evaluate f at (a+b)/2 (i.e., the midpoint of interval [a,b]), and check the sign of the result. If the result differs in sign from f(a), then find the root in the smaller interval [a,(a+b)/2]; if the result differs in sign from f(b), find the root in the interval [(a+b)/2,b]; in the highly unlikely event that f( (a+b)/2 ) is exactly equal to 0, then (a+b)/2 is the root.

Bisection is usually implemented iteratively, but the above description suggests a way to express it recursively. Do so. The base case for the recursion should be that b-a is less than some tolerance.