Finding the tangent and secant lines without using the derivatives. HELP PLEASE!!! So confused.....?

Question

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data table is graphed, the slope of the tangent line represents the heart rate in beats/min. The monitor estimates this value by calculating the slope of the secant line. Use the data (points provided) to estimate the patient's heart rate after 42 minutes using the secant line between the points with t=38 and t=42.

Points provided: (36,2540), (38,2650), (40,2880), (42,2990), (44, 3040)

Answer 1

The secant line goes through the curve at 2 points, the tangent line at one. The derivative that gets you the tangent is just the limit of the secant as the 2 points get closer together. So all the question asks for is the slope of the line through (38, 2650) and (42, 2990), and just like high school, you find the change in y (340) and the change in x (4), and divide, getting 85 beats/min.

Answer 2

♠ as a matter of fact human eye is able to assess the situation not worse than accurate mathematical calculations on a graph; and what is remarkable – rather fast! be I a nurse looking at the monitor I would report that heart rate is alarmingly falling from (2880 -2650)/2= 115 to (2990 -2880)/2=55 beats/min, the next 2 minutes proving that rate of (3040 –2990)/2 =25 means the patient is almost dying; so my answer is 55 with concern in my voice no matter what the science of math says; the number (2990 –2650)/4= 85 would sound quite innocent.

Answer 3

This equation represents a circle with a center at (2,3). hence a tangent line at any element is perpendicular to the radial line at that given element. We also understand that the slope of a line perpendicular to a unique line with slope m is -a million/m. Now enable's practice all this. The radial line at (5,a million) also passes by skill of the middle (2,3). So the slope of this line is (3-a million)/(2-5) = -2/3. So a tangent line at (5,a million) should be perpendicular to the radial line meaning the slope of the tangent line is -a million/(-2/3) = 3/2 or a million.5. Now all of us understand the slope of the line is a million.5 and all of us understand a level alongside the line (5,a million) so use element slope style to jot down the equation. (y-a million) = a million.5*(x-5)