Question
A manufacturer of handcrafted wine racks has determined that the cost to produce $x$ units per month is given by $C=0.2 x^{2}+10,000 .$ How fast is cost per month changing when production is changing at the rate of 12 units per month and the production level is 80 units?
Step 1
2x^{2}+10,000$. We want to find how fast the cost is changing with respect to time, which is $\frac{dC}{dt}$, when $\frac{dx}{dt}=12$ and $x=80$. Show more…
Show all steps
Your feedback will help us improve your experience
Daphne Pusey and 81 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Cost A manufacturer of handcrafted wine racks has determined that the cost to produce $x$ units per month is given by $C=0.2 x^{2}+10,000 .$ How fast is cost per month changing when production is changing at the rate of 12 units per month and the production level is 80 units?
Applications of the Derivative
Related Rates
A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C = 0.2x2 + 10,000. How fast is the cost per month changing when production is changing at the rate of 12 units per month and the production level is 80 units?
A manufacturer of handcrafted wine racks has determined that the cost to produce X units per month is given by C = 0.2x2 + 10,000. How fast is the cost per month changing when production is changing at the rate of 13 units per month and the production level is 80 units? Costs are increasing at the rate of $ per month at this production level. (Round to the nearest dollar as needed )
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD