The function models the cumulative number of gallons (in thousands) of water that…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The function g models the cumulative number of gallons (in thousands) of water that have flowed through a dam t hours after midnight. A calculator returns the following values for g near t=3.
Numerical data:
t (h) g(t) (thousand gal)
2.90 14.508
2.95 14.819
3.00 15.133
3.05 15.452
3.10 15.765
(a) Using appropriate numerical work based on the table, determine a single best estimate for g′(3). Clearly identify which numerical quotient you choose and show all computation.
(b) State the units of your answer from part (a) and interpret its meaning in the context of water flow through the dam.
(c) Explain how your estimate would be affected—be as specific as possible—if the tabulated values had been rounded to the nearest tenth instead of to three decimal places.