The Intermediate Value Theorem

EARNING OBJECTIVE: Use the Intermediate Value Theorem to determine the existence of a olution to $f(x)=V$ on the interval $a,b$

Let $f(x)=x^2-5x$ on $-3,1$

Use the IVT to determine if there is a solution to $f(x)=14$ in the interval between $-3$ and $1.$ If so$,$ find t value of cin the interval such that $f(c)=14.$

a$.)f(x)$ is continuous on $-3,1$

$14$ is not between $-3$ and $1$

$c=126$

b$.)f(x)$ is continuous on $-3,1$

$14$ is between $f(-3)=24$ and $f(1)=-4$

$c=-2$

e$.)f(x)$ is continuous on $-3,1$

$14$ is between $f(-3)=24$ and $f(1)=-4$

$e=-2,e=7$