Question

一道英语 微积分题 紧急求助啊！！谢谢！

It has been hypothesized that the human heart is capable of beating only a fixed number of times and then it gives up. As far-fetched as this hypothesis may be, assume it to be true for the purpose of this problem.
Oprah would like to develop a personal exercise regime that maximizes her lifespan. To do so, she wants to minimize her daily number of heart beats. She discovers that by exercising every day for T hours, her heart rate throughout the rest of the day (24 − T) can be predicted by the formula:
（见图片）
where H(T) is measured in beats per hour. During her exercise period, her heart rate is always 120 beats per minute.
Describe what the formula for H(T) says about Oprah's heart rate during the rest of the day as a function of the time (T) she spends exercising. In particular, how does the additional benefit she gets by exercising for one additional hour if she's only exercising for a short period of time compare to the benefit of an additional hour if she is exercising for a long period of time. Provide Oprah with some advice on her exercise regime. To be specific, how many hours (T) should she exercise each day?

Answer 1

问边际 函数 每增加1 小时的心跳
求导 得 H'(T)=2400* (-1)*1/(1+T)^2 =-2400*(1+T)^(-2) T>=0

这个边际纳枣皮函数 是减函数 心跳次数是有限制的 最佳情况是一天800 下 (根据积洞差分得

所以 800=2400(1+1/(1+T)) T=2

所以一天运动2小岩蚂时为佳