In problems 58 , each quotation is a statement about a quantitity of something c
ID: 2837012 • Letter: I
Question
In problems 58 , each quotation is a statement about a quantitity of something changing over time.
Let f(t) represent the quantity at time t. For each quotation, tell what f represents and whether the first and second derivatives of f are positive or negative.
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58.
(a)"The child's temperature is still rising, but slower than it was a few hours ago."
(b) "The number of whales is decreasing, but at a slower rate than last year."
(c) "The number of people with the flu is rising and at a faster rate than last month."
Explanation / Answer
(a) f represents Temperature of child at time instant t. first derivative is positive as temperature of child is increasing. second derivative is negative as rate of increase is slower than few hours ago
(b) f represents Number of whales at time t. first derivative is negative as number of whales are decreasing. second derivative is negative as rate of decrease is slower than last year.
(c) f represents number of people with flu at a time instant t. first derivative is positive as no of people with flu are increasing. second derivative is positive as rate of increase is faster than last month