Question

acme manufactures screws using labor and equipment. its total daily cost as a function of hours of operation is given by $c(h)=w(h)+r(h)$ where $w(h)$ is the labor cost and $r(h)$ is the equipment cost. at $h = 9$, suppose the labor cost is changing at a rate of $w(9)=9$ dollars per hour, and the equipment cost is changing at a rate of $r(9)=8$ dollars per hour. what is the rate of change of total cost at $h = 9$?

Explanation:

Step1: Apply derivative rule for sum

The derivative of a sum of functions $c(h)=w(h)+r(h)$ is $c'(h)=w'(h)+r'(h)$ by the sum - rule of derivatives.

Step2: Evaluate at $h = 9$

We want to find $c'(9)$. Substitute $h = 9$ into $c'(h)$. Given $w'(9)=9$ and $r'(9)=8$, then $c'(9)=w'(9)+r'(9)$.

Step3: Calculate the value

$c'(9)=9 + 8=17$.

Answer:

17