The demand function for a product $is$ modeled $byp=600-3x,0x200,$ where $pis$ the price per unit $(in$ dollars$)$ and $xis$ the number $of$ units.

$(a)$ Determine when the demand $is$ elastic and inelastic.

Determine when the demand $isof$ unit elasticity.

$(b)$ Use the result $of$ part $(a)to$ describe the behavior $of$ the revenue function.

$8$ top $1$

$(a)$ Determine when the demand $is$ elastic and inelastic. Determine when the demand $isof$ unit elasticity.

$Ifp=f(x)is$ a differentiable function, then the price elasticity $of$ demand $is$ given $by$

$=\frac{\frac{p}{x}}{\frac{dp}{dx}}$

For a given price, the demand $is$ elastic when $||>1,$ the demand $is$ inelastic when and the demand has unit elasticity when $||=1.$

$We$ are given the demand function $p=600-3x,0x200.$ First, talke the first derivative $of$ this function.

$\frac{dp}{dx}=$

Now, determine the price elastidty $of$ demand.

$=(\frac{\frac{(500-2x)}{x}}{})$

$--\frac{200}{x}+1$

Step $2$

$-\frac{200}{x}+1=-1$

$-\frac{200}{x}=-2$

$x=100$

Therefore, the demand has unit elacticity $at$ the following values. $(Enter$ your answers $as$ a comma$-$separated list.$)$

$x=$

$100$

stop $3$

$To$ summarize, state the intervals when demand $is$ elastic and inelastic.

elastic

Inelastic