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 integral from 0 to 3 of f of x, dx. 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.
I have no idea how to do this with the given information, what is the # of rectangles? how does the second derivative help?

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 integral from 0 to 3 of f of x, dx. 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.
I have no idea how to do this with the given information, what is the # of rectangles? how does the second derivative help?

anonymous · Answer

http://imgur.com/OOV2ahU

templeguy · Answer

I'll answer if you answer my question

templeguy · Answer

Why did she say "ow" at 0:13 https://www.youtube.com/watch?v=4cEH-KUjdOY

anonymous · Answer

kicked her?

anonymous · Answer

Yeah I just need an explanation of the question, Im having trouble understanding what its asking me to do, what method is there for doing this? i take very good notes but this one is giving me some trouble

anonymous · Answer

Please help

loser66 · Answer

actually, the midpoint = 1.65 but this problem is about "approximate" ,hence midpoint = 1.3439