Science:Math Exam Resources/Courses/MATH101 A/April 2025/Question 07 (b)/Statement

A small rocket propels itself straight upwards. From $t=0$ to $t=4$ minutes, its velocity is given by: $$v(t)=\frac{100}{1+t^3}\text{meters/min}.$$ When we were calculating the error of our approximation, we calculated that $$|v^{″}(t)|=\left|600t\frac{1-2t^3}{(1+t^3{)}^3}\right|\le 307200(=64\cdot 4800),$$ for all $0\le t\le 4$, which is too much. But we are dedicated and want to make our estimation work by using more trapezoids. To make our error at most 64 meters, using the bound given above, how many trapezoids would we need? Simplify your answer.