Use the Intermediate Value Theorem $to$ show that there $is$ a root $of$ the given equation $in$

the specified interval.

$x^4+x-8=0,(1,2)$

$f(x)=x^4+x-8is---$Select$---$ hat$(v)on$ the closed interval $1,2,$

$f(1)=$

$,$ and $f(2)=$

$.$ Since $c(1,2)f(c)=$hat$(v)x^4+x-8=0(1,2)-6,$ there $is$ a number $cin$

$(1,2)$ such that $f(c)=$hat$(v)by$ the Intermediate Value Theorem. Thus, there $isa$

$of$ the equation $x^4+x-8=0in$ the interval $(1,2).$

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