The graph shows the depth of water W in a reservoir over a one-year period as a

Question

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year, (Assume 365 days in a year W (ft) 100 75 50 25 100 200 300 (days) (a) Determine the intervals on which the function W is increasing. (Select all that apply (0,150) (150, 300) (300, 365) Determine the intervals on which the function W is decreasing. (Select all that apply) (0, 150) (150, 300) (200, 365) (b) At what value of x does W achieve a local maximum days At what value of x does W achieve a local minimum? days (e) Find the net change in the depth W from 100 days to 200 days.

Explanation / Answer

a) It can be easily observed from the given graph that the function is increasing in the range (0, 150) and (300, 365). It is decreasing in the range (150, 300)

b) The function achieves local maxima at x = 150 and local minima at x = 300

c) At x = 100, W = 75. At x = 200, W = 50

Net change = 75 - 50 = 25

Hence W changes by 25 ft from 100 days to 200 days.

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