Suppose that the dollar cost of producing x radios is C(x) - 400 + 20x - 0.2x2.

Question

Suppose that the dollar cost of producing x radios is C(x) - 400 + 20x - 0.2x2. Find the marginal cost when 30 radios are produced. S820 $820 S32 The total cost to produce x handcrafted wagons is C(x)= 60 + 2x - x^2 + 5x^3. Find the rate of change of cost with respect to the number of wagons produced (the marginal cost) when x = 5. $670 per wagon $427 per wagon $610 per wagon $367 per wagon 10) The polynomial C(x) = -0.006x^4 + 0.140X3 - 0.53x^2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Find the rate of change of concentration with respect to time. A) = -0.024x^4 + 0.420x3 - 1.06x2 + 1.79x B) = -0.018x^3 + 0280x^2 - 053x + 1.79 Q ~ = -0.006X3 + 0.140x2 - 053x + 1.79

Explanation / Answer

Marginal cost is the instantaneous rate of change of cost relative to production at a given production level.

when c(x) is the cost of producing x items,then dc/dx will be the marginal cost at the production level x.

so

1.c(x) = 400+20x-(0.2)x2

so dc/dx = 20-(0.4)x,so at x = 30

marginal cost = $8

2.c(x) = 60+2x-x2+5x3

so dc/dx = 2-2x+15x2

at x = 5,

marginal cost = $367 per wagon

3.here we have to find dc/dt,so by differentiating c with respect to x we get dc/dx which is same as dc/dt

so dc/dx =(-0.024)x3+(0.420)x2-(1.06)x+(1.79)

4.f(2) = (-8)2(-1)+5(2)(-2)

f(2) = (-11/4)

here options are not matching,but i think that my solution is correct,there may be some problem with solutions.

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