Section $2\mathrm{.}3,$ Page $110,$ #$37$B$.$ Cost function. The cost, in dollars, of producing $x$ units of a certain commodity is $C(x)=630025x0\mathrm{.}048x^2.$

$($a$)$ Find the average rate of change of $C$ with respect to $x$ when the production level is changed from $x=50$ to $x=60.$ Show the formula and work.

$($b$)$ Find the instantaneous rate of change of $C$ with respect to $x($the marginal cost$)$ when $x=50.$ Show the formula and work.