a$.$ Use the Intermediate Value Theorem to show that the following equation has a solution on the given interval.

b$.$ Use a graphing utility to find all the solutions to the equation on the given interval.

c$.$ Illustrate your answers with an appropriate graph.

$3x^3+x-1=0$;$(0,1)$

The value of the function at the right endpoint is

$($Type an integer or decimal rounded to three decimal places as needed.$)$

Why can the Intermediate Value Theorem be used to show that the equation has a solution on $(0,1)?$

A$.$ It can be used because $f(x)=3x^3+x-1$ is continuous on $0,1$ and the function is defined at $x=0$ and $x=1.$

B$.$ It can be used because $f(x)=3x^3+x-1$ is defined on $(0,1)$ and $f(x)=3x^3+x-10,1f(0)f(1)f(x)=3x^3+x-1(0,1)(0,1)x$~~$-1,2,1-10,10,1f(0).$

$b.$ There $i\frac{s}{a}re$ a solution$(s)to$ the equation $in(0,1)atx$~~ $$

$(Typean$ integer $or$ decimal rounded $to$ three decimal places $as$ needed. Use a comma $to$ separate answers $as$ needed$)$

$c.$ Choose the correct graph below. The window setting $is$ for each graph $is-1,2,1by-10,10,1.$

$A.B.c\mathrm{.}0.$

$C.It$ can $be$ used because $f(x)=3x^3+x-1is$ continuous $on0,1$ and $0is$ between $f(0)$ and $f(1).$

$D.It$ can $be$ used because $f(x)=3x^3+x-1is$ defined $on(0,1)$ and $f(0).$

$b.$ There $i\frac{s}{a}re$ a solution$(s)to$ the equation $in(0,1)atx$~~ $$

$(Typean$ integer $or$ decimal rounded $to$ three decimal places $as$ needed. Use a comma $to$ separate answers $as$ needed$)$

$c.$ Choose the correct graph below. The window setting $is$ for each graph $is-1,2,1by-10,10,1.$

$A.B.c.$