What is the formula for the slope of a secant line?
For unlimited access to Homework Help, a Homework+ subscription is required.
The point lies on the curve .
If Q is the point , use your calculator to find the slope of the secant line PQ ( correct to six decimal places) for the following values.
0
0.4
0.49
0.499
1
0.6
0.51
0.501
Using the results of part (a), guess the value of the slope of the tangent line to the curve at
Using the slope from part (b), find an equation of the tangent line to the curve at .
Sketch the curve, two of the secant lines, and the tangent line.
:- A curve has equation y = f(x)
Write an expression for the slope of the secant line through the points
P(3,f(3)) and Q(x,f(x))
Write an expression for the slope of the tangent line at P.
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 in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute.
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.
What are your conclusions?