# Help applying the intermediate value theorem

• May 3rd 2009, 08:09 PM
Livingg90
Help applying the intermediate value theorem
Show that the equation x^3=5 has a solution on the interval [1,2]
• May 3rd 2009, 08:14 PM
TheEmptySet
Quote:

Originally Posted by Livingg90
Show that the equation x^3=5 has a solution on the interval [1,2]

Consider the function

$f(x)=x^3-5$ and note that

$f(1)=1^3-5=-4$ and

$f(2)=2^3-5=3$

Since polynomials are continous by the intermediate value theorem there exists $c \in (1,2)$ such that $f(c)=0$

$f(c)=0=c^3-5$ so the equation has a solution