## College Algebra (10th Edition)

$f(a)=f(1.4)=-0.1754\lt 0$ and $f(b) =f(1.5)=1.4063\gt 0$ Since function values have opposite signs at the endpoints of the interval, by the Intermediate Value Theorem, there is at least one real zero of $f$ between $1.4$ and $1.5.$
Intermediate Value Theorem Let $f$ be a polynomial function. If $a\lt b$ and if $f(a)$ and $f(b)$ are of opposite sign, there is at least one real zero of $f$ between $a$ and $b.$ --- Using a calculator, $f(a)=f(1.4)=-0.1754\lt 0$ and $f(b) =f(1.5)=1.4063\gt 0$ Since function values have opposite signs at the endpoints of the interval, by the Intermediate Value Theorem, there is at least one real zero of $f$ between $1.4$ and $1.5.$