Consider the function on the interval has at least one zero in (actually f(1)=0) so show that has *exactly* on zero in the indicated interval. Hint:Use the Mean Value Theorem/Rolle's Theorem to prove the result.
Consider the function on the interval has at least one zero in (actually f(1)=0) so show that has *exactly* on zero in the indicated interval. Hint:Use the Mean Value Theorem/Rolle's Theorem to prove the result.
if had more than one zero in [1/2, 2], then by Rolle's theorem would have at least one root in [1/2, 2]. but the (real) root of is