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
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