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CalculusQ&A LibraryThe cost of purifying a gallon of water to a purity of x percent is shown below.C(x) = 100100 − 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.Question

Asked Oct 3, 2019

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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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