0 3 7 10 12 (days) r'(t) (centimeters per day) -6.1 -5.0 -4.4 -3.8 -3.5 4. An ice sculpture melts in such a way that it can be modeled as a cone that maintains a conical shape as it decreases in size. The radius of the base of the cone is given by a twice-differentiable function r, where r(t) is measured in centimeters and t is measured in days. The table above gives selected values of r'(t), the rate of change of the radius, over the time interval 0 ≤ ≤ 12. (a) Approximate r"(8.5) using the average rate of change of r' over the interval 7 ≤ ≤ 10. Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time 1, 0 ≤ 1 ≤ 3, for which r'(t) = -6 ? Justify your answer.
0 3 7 10 12 (days) r'(t) (centimeters per day) -6.1 -5.0 -4.4 -3.8 -3.5 4. An ice sculpture melts in such a way that it can be modeled as a cone that maintains a conical shape as it decreases in size. The radius of the base of the cone is given by a twice-differentiable function r, where r(t) is measured in centimeters and t is measured in days. The table above gives selected values of r'(t), the rate of change of the radius, over the time interval 0 ≤ ≤ 12. (a) Approximate r"(8.5) using the average rate of change of r' over the interval 7 ≤ ≤ 10. Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time 1, 0 ≤ 1 ≤ 3, for which r'(t) = -6 ? Justify your answer.
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Transcribed Image Text:1
0
3
7
10 12
(days)
r' (t)
-6.1 -5.0-4.4 -3.8 -3.5
(centimeters per day)
4. An ice sculpture melts in such a way that it can be modeled as a cone that maintains a conical shape as it
decreases in size. The radius of the base of the cone is given by a twice-differentiable function r, where r(t) is
measured in centimeters and t is measured in days. The table above gives selected values of r'(t), the rate of
change of the radius, over the time interval 0 ≤ 1 ≤ 12.
(a) Approximate r"(8.5) using the average rate of change of r' over the interval 7 ≤ i ≤ 10. Show the
computations that lead to your answer, and indicate units of measure.
(b) Is there a time 1, 0 ≤ 1 ≤ 3, for which r'(t) = -6 ? Justify your answer.
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