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

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

Steve · Answer

f is positive, increasing, and concave up. Draw such a curve, and you can see which approximations over- and under-estimate the value.