$3,260$

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$$ TANAPCALCBR$103\mathrm{.}1\mathrm{.}058.$MI$.$

Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by

$p=f(x)=-0\mathrm{.}1x^2-0\mathrm{.}3x+28$

where $x$ is the quantity demanded in thousands and $p$ is the unit price in dollars.

$($a$)$ Find $f^{\text{'}}(x).$

$f^{\text{'}}(x)=$

$($b$)$ What is the rate of change of the unit price $($in dollars per $1,000$ lamps$)$ when the quantity demanded is $8,000$ units