Question

If you're GOOD with MATH, and understand it really well, I need some help! I'm REALLY really confused about this stuff: The Tangent and Velocity Problems

Answer 1

Here's the Question:
A Cardiac Monitor is used to measure the heart rate of a patient after surgery. It complies the number of heartbeats after t minutes. When the data is graphed, as shown in the below table, the slope of the tangent line represents the heart rate in beats per minutes.


Then the question states, the monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of t.

I need to find these...

a) t=36 & t=42
b) t=38 and t=42
....

WHAT is the question asking and what am I supposed to do? Please help me!

Answer 2

The table:

t (min) Heartbeats
36 2530
38 2661
40 2806
42 2948
44 3080

Answer 3

the slope of the secant line is the gradient of the chord between two points on the curve.

so we would do (2948-2530)/(42-36)

Answer 4

for a)

Answer 5

gradient of secant line =

\[\frac{f(x_2) - f(x_1)}{x_2- x_1}\]