+69 1) f(x)>0, f'(x)<0, and f''(x)>0 for all values of x. If RRAM is used to approximate ∫f(x)dx from x= 0 to 4, is it an over estimate, under estimate, or is it impossible to tell with the given information. Justify your answer.
2) If if a trapezoidal rule was used for the approximation as described in problem 1, would the resulting approximation be an over estimate, under estimate, or is it impossible to tell with the given information. Justify your answer.
+33661 1). Underestimate. The curve is always positive, it decreases to the right but the decrease reduces. Rectangles started from the right are therefore always under the curve. Think of the function e^ -x for example.
2). Overestimate. The straight line joining at the tops of the trapezoids are always use above the curve.
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