Need help to estimate the slope of the tangent line at P(3,2.8)

Question

Below is the whole question. All of the data in "a.)" is correct. I need help finding the slope of the tangent line at P (3, 2.8). This is part "b" in bold below.

The experimental data in the table below define y as a function of x

X= 0 1 2 3 4 5

Y= 3.7 2.7 2.5 2.8 3.3 4.3

a.) Let P be the point (3,2.8). Complete the table below by computing the slope of the secant line PQ when Q is the point of the graph with x-coordinate x1

If x1=0, the slope of PQ is: -0.3

If x1=1, the slope of PQ is: 0.05

If x1=2, the slope of PQ is: 0.3

If x1=4, the slope of PQ is: 0.5

If x1=5, the slope of PQ is: 0.75

b.) Draw the graph of the function for yourself and estimate the slope of the tangent line at P(3,2.8)

Answer:

Answer 1

The point of this exercise is to visualize that the slope of the tangent

can be obtained by slopes of the secant lines as they get tighter and tighter

around the point x=3.

If you draw the graph you will probably find that the slope of the tangent

is around 0.4.

Note that the slopes of secants for x=2 and x=4 are closer to the

tangent, than secants for x=0 or x=5.

I do not know how the teacher expects you to estimate the slope of the tangent.

A common way is to take the average between the slopes for neighboring

secants for x=2 and x=4.

Another way is to estimate the tangent as the secant connecting the pair of points

(2, 2.5) and (4, 3.3).