Monitor my heart rate

Recall the Intermediate Value Theorem (IVT):

For a continuous function $f$ on the interval $[a, b]$ , there exists a value $y_0$ between $f(a)$ and $f(b)$ for every number $x_0$ between $a$ and $b$ such that $f(x_0) = y_0$ . Intuitively, what that translates to is for continuous variables like time, temperature, or distance, to get from point $B$ to point $Y$ , you must have crossed points $C, D, E... V, W, X$ to get there. What this doesn't guarantee, on the other hand, is that you crossed $A$ and $Z$ , since those are outside of the range $(B, Y)$ that IVT guarantees you "crossed."

In this example, our domain is time, [7:00, 7:30], and our range is heart rate measured in beats per minute, $(125, 165)$ . Because our function, heart rate as a function of time, is continuous, IVT guarantees that Pi's heart rate must have been all heart rates between $125$ and $165$ bpm at some point on the time interval [7:00, 7:30]. What the IVT, then, doesn't guarantee is that her heart rate was any value $\leq 125$ and $\geq 165$ , so our answer is $\boxed{170}$ .

We know that 130, 140, 150, and 160 have been shown by the Fitbit as the heartbeat increased from 125 to 165. We do not know if the heartbeat has increased to at least 170 during the run as the information we get is only at the start and the end of the run. Thus, 170 is the answer.

This is not a solution but an idea came to my mind, you said at the beginning the fibit gave you a record of 125 and at the end 165 so 170 is not possible choice, hopefully right.