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1) If the total cost function for a product is: C(x) = 250 + 6x + 0.1x 2 dollars

ID: 2962976 • Letter: 1

Question

1) If the total cost function for a product is: C(x) = 250 + 6x + 0.1x2 dollars; find the minimum value for the average cost per unit. The minimum average cost per unit for this function is ______________ dollars per unit ?



2) Find the equation for the tangent line to the function f(x) = 4x3+3x2+5x+6 when x = 2.

Put your answer in slope intercept (y= mx+ b) format, and use it to identify the y-intercept for this line.

The y-intercept for the tangent line to the function     f(x) = 4x3+3x2+5x+6 when x = 2 is

Explanation / Answer

1) c(x)/x = 250/x + 6 +0.1x


differentiating and equating it to zero


-250/x^2 +0.1 = 0



x = 50


so c(50)/50 = 5 + 6 +5



min = 16 dolllars per unit



2)f'(x) = 12x^2 +6x+5


f'(2) = 65



y = 60


so eq = (y - 60) = 65(x-2)


y = 65x -70




y-intercept = -70