The cost of purifying a gallon of water to a purity of x percent is shown below. C(x) = 100 100 − x cents for 50 ≤ x < 100 (a) Find the instantaneous rate of change of the cost with respect to purity. C'(x) = −100(100−x2)+1100−x (b) Evaluate this rate of change for a purity of 95%. C'(95) = centsInterpret your answer. The cost is ---Select--- increasing decreasing by this amount per additional percent of purity. (c) Evaluate this rate of change for a purity of 98%. C'(98) = centsInterpret your answer. The cost is ---Select--- increasing decreasing by this amount per additional percent of purity.
The cost of purifying a gallon of water to a purity of x percent is shown below. C(x) = 100 100 − x cents for 50 ≤ x < 100 (a) Find the instantaneous rate of change of the cost with respect to purity. C'(x) = −100(100−x2)+1100−x (b) Evaluate this rate of change for a purity of 95%. C'(95) = centsInterpret your answer. The cost is ---Select--- increasing decreasing by this amount per additional percent of purity. (c) Evaluate this rate of change for a purity of 98%. C'(98) = centsInterpret your answer. The cost is ---Select--- increasing decreasing by this amount per additional percent of purity.
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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The cost of purifying a gallon of water to a purity of x percent is shown below.
C(x) =
cents for
| 100 |
| 100 − x |
50 ≤ x < 100
(a) Find the instantaneous rate of change of the cost with respect to purity.
(b) Evaluate this rate of change for a purity of 95%.
Interpret your answer.
(c) Evaluate this rate of change for a purity of 98%.
Interpret your answer.
C'(x) =
−100(100−x2)+1100−x
(b) Evaluate this rate of change for a purity of 95%.
C'(95)
= centsInterpret your answer.
The cost is ---Select--- increasing decreasing by this amount per additional percent of purity.
(c) Evaluate this rate of change for a purity of 98%.
C'(98)
= centsInterpret your answer.
The cost is ---Select--- increasing decreasing by this amount per additional percent of purity.
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