calculus question

Question

 

Given f(x) > 0 with f ′ (x) > 0, and f ″ (x) > 0 for all x in the interval [0, 3] with f(0) = 0.1 and f(3) = 1, the left, right, trapezoidal, and midpoint rule approximations were used to estimate . The estimates were 0.8067, 0.9635, 1.0514, 1.0753 and 1.3439, and the same number of subintervals were used in each case. Match the rule to its estimate. (5 points)

				1.	trapezoidal
				2.	right endpoint
				3.	actual area
				4.	midpoint
				5.	left endpoint
a.	0.8067
b.	1.3439
c.	0.9635
d.	1.0753
e.	1.0514

Answer 1

Because the given function is increasing and concave up, I think we would have, from least to greatest:

Left-hand rectangles < Midpoint rectangles < Actual area < Trapezoids < Right-hand rectangles

5a , 4c , 3e , 1d , 2b