07:43
Calculus: Graphical, Numerical, Algebraic
cost, Revenue, and Profit A company can manufacture $x$ items at a cost of $c(x)$ dollars, a sales revenue of $r(x)$ dollars and a profit of $p(x)=r(x)-c(x)$ dollars (all amounts in thousands). Find $d c / d t, d r / d t,$ and $d p / d t$ for the following values of $x$ and $d x / d t$
(a) $r(x)=9 x, \quad c(x)=x^{3}-6 x^{2}+15 x$
and $d x / d t=0.1$ when $x=2 .$
(b) $r(x)=70 x, \quad c(x)=x^{3}-6 x^{2}+45 / x$
and $d x / d t=0.05$ when $x=1.5$