suppose that the total cost function for a manufacturer is C=100+X^2

Question

where x represents the weekly production of widgets. if production is increasing at the rate of 500 calculators per week, when production output is 6000 calculators. find the rate of increase in cost.

Answer 1

dx/dt = 500

dc/dx = 0 + 2 x

dc/dt = dc/dx * dx/dt

= 2 x * 500
so at x = 6000
dc/dt = 12,000 * 500

Answer 2

6000000