(i) Discuss the continuity of the function f(x) = {x2²− 3x if x < 2 2x + 4 if x ≥ 2 on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2.(ii) An efficiency study of the morning shift at a certain factory indicates that an averageworker arriving on the job at 7: 00 A. M. will have assembled f (x) = x3 + 6x2 + 15xunits x hours later. Approximately how many units will the worker assemblebetween 8: 00 and 8: 15 A. M. ?(iii) A manufacturer’s total cost is C(q) = 0.1q3 + 0.5q2 + 500q + 200dollars when the level of production is q units.The current level of production is 4 units, and the manufacturer is planning to increase this to4.1 units. Estimate how the total cost will change as a result.
(i) Discuss the continuity of the function f(x) =
- {x2²− 3x if x < 2
2x + 4 if x ≥ 2
on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2.
(ii) An efficiency study of the morning shift at a certain factory indicates that an average
worker arriving on the job at 7: 00 A. M. will have assembled f (x) = x
3 + 6x
2 + 15x
units x hours later. Approximately how many units will the worker assemble
between 8: 00 and 8: 15 A. M. ?
(iii) A manufacturer’s total cost is C(q) = 0.1q
3 + 0.5q
2 + 500q + 200
dollars when the level of production is q units.
The current level of production is 4 units, and the manufacturer is planning to increase this to
4.1 units. Estimate how the total cost will change as a result.
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