I think you're right on a and b. On c, I think you're right about f prime (the first derivative), but I think f'', the second derivative, is also positive. The rate is also increasing.
I am new to calculus so please excuse my basic questions. Our teacher is a hard on us and she always wants explanations with each problem. HW is like a quiz based on accuracy so I am trying my best to get everything correct.
Here is the problem:
Each quotation is a statement about a quantity 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 and why.
My answers (please check and add explanation if mine is inadequate or inaccurate so I can learn):
a.) "The child's temperature is still rising, but slower than it was a few hours ago." For this quotation, f represents the child's temperature; f prime is positive since the temperature of the child is rising (f), f double prime is negative since the graph is concave down.
b.) "The number of whales is decreasing, but at a slower rate than last year." For this quotation, f represents the number of whales; f prime is negative since the number of whales is decreasing (f), f double prime is positive since the graph is concave up.
c.) "The number of people with the flu is rising and at a faster rate than last month." For this quotation, f represents the number of people with the flu; f prime is positive since the number of people with the flu is rising (f), f double prime is negative since the graph is concave down.