Given that f"(t) < 0 on the interval [a, b], what can be said ...

[Lobcity]

Question 1

The following table gives values of an unknown function  f(x)  determined by experimental measurement. Find the best  Midpoint Rule approximation you can for dx based on the values given in the table.

x	f(x)
2.00	1.052
2.25	1.042
2.50	1.034
2.75	1.026
3.00	1.020
3.25	1.016
3.50	1.012
3.75	1.010
4.00	1.008

◦ M₄  =  2.0460
◦ M₄  =  2.0470
◦ M₄  =  2.0465
◦ M₄  =  2.0480
◦ M₄  =  2.0475

Question 2

Given that  f"(t) < 0  on the interval  [a, b],  what can be said about  the relationship between the values of  the integral   I  = dx,  the Trapezoid Rule approximation  T_n  for  I, and the Midpoint Rule approximation  M_n  for  I?
◦ I  <  M_n  <  T_n
◦ M_n <  I  <  T_n
◦ T_n <  M_n <  I
◦ T_n <  I  <  M_n
◦ It is impossible to tell.

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[Lobcity]

YES! Correct, THANKS for helping me on my review

[LegendaryAnswers]

Thanks for the timely response, appreciate it