AB Calculus Question about tangent line approximation. I don\'t even know how to
ID: 2851108 • Letter: A
Question
AB Calculus Question about tangent line approximation. I don't even know how to start this page and it would be greatly appreciated if someone could explain it.
Due to a bad storm on a low-lying road, a large circular puddle of water forms. The area of the puddle increases as the storm intensifies. The radius of the puddle, in feet, is modeled by a twice-differentiable function r of time t, where t is measured in minutes. For 0 < t < 15, the graph of r is concave up. The table below gives selected values of the rate of change, r’( t) of the radius of the puddle over the time interval 0 t 15. The radius of the puddle is 7 feet when t = 6.
t (minutes)
0
3
6
8
11
12
15
r ‘( t) (feet per minute)
1.2
2.3
3.4
4.3
4.9
5.0
6.2
a. Estimate the radius of the puddle when t = 5 using the tangent line approximation at t = 6. Is your estimate greater than or less than the true value? Give a reason for your answer.
b. Find the rate of change of the area of the puddle with respect to time at t = 6. Indicate units of measure.
c. Use a right Riemann sum with six intervals using the data in the table to approximate (integral) r’(t) dt. Using correct units, explain the meaning of (integral) r’(t) dt in the context of the problem situation.
d. Is your approximation in part c) greater or less than (integral) r’(t) dt? Give a reason for your answer.
NOTE all r'(t) dt are integrated from 0 to 15
t (minutes)
0
3
6
8
11
12
15
r ‘( t) (feet per minute)
1.2
2.3
3.4
4.3
4.9
5.0
6.2
Explanation / Answer
AB Calculus Question about tangent line approximation. I don't even know how to