Help applying the intermediate value theorem

**Livingg90** · May 3rd 2009, 07:09 PM

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

**TheEmptySet** · May 3rd 2009, 07:14 PM

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

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